Research ArticleCredit Risk Prediction Using Fuzzy Immune Learning
Ehsan Kamalloo and Mohammad Saniee Abadeh
Faculty of Electrical and Computer Engineering Tarbiat Modares University Tehran 14115-143 Iran
Correspondence should be addressed to Mohammad Saniee Abadeh sanieemodaresacir
Received 5 February 2014 Revised 1 June 2014 Accepted 6 June 2014 Published 24 June 2014
Academic Editor M Onder Efe
Copyright copy 2014 E Kamalloo and M Saniee Abadeh This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
The use of credit has grown considerably in recent years Banks and financial institutions confront credit risks to conduct theirbusiness Good management of these risks is a key factor to increase profitability Therefore every bank needs to predict the creditrisks of its customers Credit risk prediction has been widely studied in the field of data mining as a classification problem Thispaper proposes a new classifier using immune principles and fuzzy rules to predict quality factors of individuals in banks Theproposed model is combined with fuzzy pattern classification to extract accurate fuzzy if-then rules In our proposed model wehave used immune memory to remember good B cells during the cloning process We have designed two forms of memory simplememory and k-layer memory Two real world credit data sets in UCI machine learning repository are selected as experimental datato show the accuracy of the proposed classifier We compare the performance of our immune-based learning system with resultsobtained by several well-known classifiers Results indicate that the proposed immune-based classification system is accurate indetecting credit risks
1 Introduction
Banks and financial agencies employ credit scoring modelsextensively to determine good and bad credits Loans are usu-ally the most significant cause of risk in banks Using creditscoring will reduce the time of loan approval procedure [1]and save cost per loan and enhance credit decisions Thisenhancement helps lenders to guarantee that they are apply-ing the same criteria to same groups of borrowers [2] In thesesituations banks can supervise the existing loans much easierthan before [3] Because of the fast growth of autofinancingin the last two decades the use of data mining for creditrisk prediction increases rapidly [4ndash7]The first investigationinto credit scoring was started by Olson and Wu in 2010 toclassify credit applications as good or bad payers [8] Fair andIsaac presented a credit scoring model in the early 60s [9]Since then various models have been developed using tradi-tional statistical methods such as discriminant analysismeth-od in [10 11] Ordinary linear regression has also been used asanother traditional statistic method for credit scoring [12 13]Recent techniques of credit risk assessment [14ndash20] treat
lending decision problem as a binary classification problem[8]
The performance of bioinspired algorithms like artificialneural networks and evolutionary computation for variousdatamining problems has been demonstrated bymany inves-tigations previously [21ndash25] Many bioinspired algorithmshave been proposed for credit scoring [1 21 26] Recently arti-ficial immune systems (AIS) have been successfully employedin a wide variety of application areas Artificial immunesystems are computational systems inspired by the processesof the natural immune systemThismetaheuristic emerged inthe 90s as a new computationalmodel in AI Hunt and Cookeapply AIS to pattern recognition problems in 1996 [27]Timmis and Knight define AIS as ldquoadaptive systems inspiredby theoretical immunology and observed immune functionsprinciples andmodels which are applied to problem solvingrdquo[28] There are various types of AIS and researchers workedmostly on the theories of immune networks clonal selectionand negative selection [29] In this paper we have proposedanAIS-based classification systemwith a new clonal selection
Hindawi Publishing CorporationAdvances in Fuzzy SystemsVolume 2014 Article ID 651324 11 pageshttpdxdoiorg1011552014651324
2 Advances in Fuzzy Systems
algorithmWithin the proposed AIS fuzzy logic has been ap-plied to extract interpretable fuzzy rules [30 31]
Themain reason that encouraged us to use the AIS meta-heuristic for credit risk prediction problem is that AIS has anature which we can use it for our problem effectively Thisnature is that AIS tends to explore the search space of theproblem very efficientlyThis capability is associated with thehypermutation operator of AIS We have selected AIS forcredit scoring prediction problem because previous investi-gations show that the so-called classification problem has avery explorative search space We have experienced thisnature of credit scoring classification problem in our experi-ments vividly The main observation which shows the explo-rative nature of this problem is that the fitness function out-puts changes drastically for very similar inputs MoreoverAIS has proved its high performance for two-class classifica-tion problems in previous investigations
The new proposed classification system in this paper is animproved version of fuzzy artificial immune system (FAIS)[30] and comprehensible credit scoring- FAIS (CCS-FAIS)[31] classifiers as the two previous versions of AIS-based clas-sification system for credit risk prediction In our proposedmodel we have employed immune memory to remembergood B-cells during the cloning process We have designedtwo forms of memory simple memory and 119896-layer memoryResults demonstrate that our new definition of memory forAIS-based fuzzy rule extraction increases the final classifi-cation rate of credit scoring process considerably The WekaDataMining tool [32] has been used to compare our classifierwith several well-known classifiers
The rest of this paper is organized as follows Section 2discusses some algorithms presented for credit risk predic-tion problem In Section 3 we describe immune systemsand the concepts we have used in our proposed algorithmSection 4 describes pattern classificationwith fuzzy logicTheproposed algorithm is presented in Section 5 Section 6 pro-vides information of performed experiments and achievedresults Finally Section 7 concludes the paper
2 Literature Review
SVM is one of the popular learning methods presented forcredit scoring classification problem Choosing the optimalinput feature subset and setting the best kernel parameters arethe two problems that should be solved to propose an efficientSVM-based classifier [33] Zhang et al [3] and Huang et al[33] used SVM for credit scoring They show that SVM has ahigh and acceptable accuracy for this classification problem
Hybrid data mining approaches also have been proposedfor effective credit scoring Yao [34] used neighborhoodrough set and SVM as a hybrid classifier In this classifier aneighborhood rough set has been employed for feature selec-tion Zhang et al [35] proposed hybridmodel based on genet-ic programming (GP) and SVM This model used GP to ex-tract if-then rules and for remaining instances of dataset itemployed discriminator based on SVM Yi [36] used a com-bination of decision tree and simulated annealingmethods tobuild a model In this hybridization authors have combined
local search strategy of decision tree algorithms and globaloptimization of simulated annealing algorithm
Exploring new techniques in credit scoring performanceimprovement can save too much money In recent yearsmany bioinspired algorithms are presented for solving clas-sification problems such as credit card fraud detection [37]credit scoring security and other applications [38] Amongthese approaches AIS is one of the newest methods that hasbeen applied for the credit scoring purposes Leung et al [9]proposed a simple AIS (SAIS) algorithm that adopted few keyconcepts of AIS (affinity measure cloning and mutation)They found SAIS a very competitive classifier
Fuzzy logic has been used for designing classificationsystems drastically [39 40]The important advantage of fuzzylogic is its influential capability in managing uncertainty andvagueness [41]Most of fuzzy classifiers generate a list of fuzzyif-then rules These rules are represented in linguistic formsthat make them interpretable by users Experts can validateand correct the rules This increases the interaction withusers Lei and Ren-hou [42] proposed a classifier based onimmune principles and fuzzy rules They apply their algo-rithm on 15 well-known UCI machine learning repository[43] data sets and achieve high accuracy The fuzzy AIS termin our proposed method is similar to Lei and Ren-houmethodThemajor difference between our proposedmethodand Lei and Ren-hou algorithm is in the definition of fitnessfunctionThey used a simple function as fitness function butwe have improved fitness function by extra terms This func-tion has been discussed in Section 5 in detail
3 Immune Systems
Researchers have been inspired by biology in solving com-putational problems There have been several techniques onbiologicalmetaphors such as evolutionary algorithms swarmintelligence and neural networks [29] Artificial immune sys-tems are bioinspired algorithms that have been active andprolific over the last decade [44 45] The basis of AIS is hu-man immune system which exploits learning and memoriz-ing capabilities of immune systems [46] Timmis et al pro-posed the relation of immunology and computation [29] atthe 80sHunt andCooke investigated the nature of learning inthe immune system and proposed a learning algorithm [27]Timmis and Knight [28] de Castro and von Zuben [47] andDasgupta [48] developed basic models of artificial immunesystems which are the sources of current AIS algorithms Im-mune-inspired models have been applied on wide variety ofresearch fields ranging frompattern recognition such as clas-sification and clustering anomaly detection [49 50] and op-timization [51 52] to robotics [53 54] and image processing[55 56] The key characteristics of immune systems arelearning adaptability memory mechanisms and self-organ-ization which are desirable to inspired algorithms Clonal se-lection immune networks and negative selection are thethree main immunological theories that are employed asstrongly accepted perspectives in AIS
Advances in Fuzzy Systems 3
Class is cAttribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5 Attribute n
S DC L DC DC ML
rArr
Figure 1 A sample fuzzy rule which is ldquoif Attribute 1 is Small and Attribute 3 is Large and Attribute 119899 is Medium Large then class is 119888rdquo
31 Natural Immune System The human immune system is adistributed pattern detection system with many functionalcomponents located in specific parts throughout the bodyThe immune system controls defense mechanism throughinnate and adaptive responses [57] Innate responses areagainst any invaders that enter the body but adaptive re-sponses are directed against particular invaders and demon-strate learning recognition memory acquisition and self-regulations of the body These invaders that infect the bodyare called antigens Antigens provoke the immune responsesThe core of adaptive responses is lymphocytes which are pro-vided with a sort of receptors to recognize antigens Lympho-cytes are divided into two types as B cells and T cells In thecase of invasion appropriate B cells attempt to clonewith pro-ducing sufficient proteins to remove antigens (called antibod-ies) A B cell holds antibodies on its shell which can identifythe antigens invading the body The matching between anti-gen and antibody is complementary and is similar to ldquolockand keyrdquo [58] T cells do not interact with antigens directlyThey circulate through the body and scan the surface of bodycells for the presence of foreign antigens that have been com-bined with the cell Then T cells bind to these cells and be-come activated Activated T cells secrete some chemicals asalert signals to others B cells which take these signals fromthe T cells become stimulated with the detection of antigenby their antibodies
32 Clonal Selection Theory The clonal selection theorydescribes the basic response of the adaptive immune systemto an antigenic stimulus The idea is that only those cellsthat are capable of detecting the antigen will proliferate andothers cannot clone This theory applies for both T cells andB cells Before the receptor of B cells binds to an antigen andB cells become stimulated and differentiate into memorycells colonies of B cells are created During the cloning pro-cess B cells undergo somatic hypermutation which keepsthe diversity of B cell population for future strange antigensAfter cloning activated B cells (or memory cells) producehuge amounts of antibodies which results in elimination ofthe antigen Some of memory cells remain within the host togenerate a rapid response upon a subsequent encounter withthe same or similar antigen [29] CLONALG [59] and B cellalgorithm [60] are AIS algorithms which are based on clonalselection theory These algorithms have cloning mutationand selection operators which makes them similar to geneticalgorithms
4 Fuzzy Rule-Based Pattern Classification
In this section we briefly explain the fuzzy rule-based patternclassification method which was first proposed by Ishibuchi
et al [61] and used in many investigations [30 31 42 62ndash65] This method consists of fuzzy rule generation and fuzzyreasoning procedures
41 Fuzzy Rule Generation Let us assume that the patternspace is 119899-dimension continuous space with 119888 classes Forsimplicity each dimension must be in the unit interval [0 1]The training data set includes 119898 labeled patterns which isshown in
119883119901 = (1199091199011 1199091199012 119909119901119899) class is 119888119870
119901 = 1 2 119898 119870 = 1 2 119888
(1)
The purpose is generating fuzzy if-then rules with the fol-lowing form Rule 119877119894 if 1199091199011 is 119860 1198941 and and 119909119901119899 is 119860 119894119899then 119883119901 belongs to Class 119862119894 with CF = CF119894 where 119877119894 is thelabel of the 119894th fuzzy if-then rule 119860 1198941 119860119894119899 are antecedentfuzzy sets in the unit interval [0 1] 119862119894 is the resultant classand CF119894 is the certainty factor (or rule weight) of the fuzzy if-then rule 119877119894 which is a real number in the unit interval [0 1](Figure 1 demonstrates a sample fuzzy if-then rule) Theremight have been some do not care antecedents in the rules andthese antecedents are usually omittedTherefore the numberof antecedents of a rule is less than or equal to 119899 Some rulesmay have a few antecedent conditions which makes themmore understandable to users
We have used a typical set of linguistic values as ante-cedent fuzzy sets The membership function of each lin-guistic value is obtained by homogeneously partitioning thedomain of each attribute into symmetric triangular fuzzy sets(119891membership in (2))We use such simple specification in exper-iments to demonstrate the high performance of our fuzzyclassifier system even if the membership function of eachantecedent fuzzy set is not tailored However we can use anytailored membership function in our fuzzy classifier systemfor a particular pattern classification problem Consider
119891membership (119909) =
minus4119909 + 1 0 le 119909 lt 0125 997904rArr S4119909 0125 le 119909 lt 025 997904rArr MSminus4119909 + 2 025 le 119909 lt 0375 997904rArr MS4119909 minus 1 0375 le 119909 lt 05 997904rArr Mminus4119909 + 3 05 le 119909 lt 0625 997904rArr M4119909 minus 2 0625 le 119909 lt 075 997904rArr MLminus4119909 + 4 075 le 119909 lt 0875 997904rArr ML4119909 minus 3 0875 le 119909 le 1 997904rArr L
119891membership (DC) = 1 forall119909 isin [0 1]
(2)
where S MS M ML L and DC respectively stand forsmall medium small medium medium large large and do
4 Advances in Fuzzy Systems
Step 1 for each pattern119883119901 do(11) Compatibility 120583119894(119883119901) = prod
119899
119895=1119891membership(119909119901119895)
Step 2 for each class ℎ do(21) Calculate relative sum of compatibility grades 120573ℎ(119877119894) = (sum
Step 3 Find class ℎ which has maximum 120573ℎ (119877119894)Step 4 119862119865119894 = (120573
ℎ(119877119894) minus 120573)(sum
119888
ℎ=1120573ℎ(119877119894)) where 120573 = (sum
119888
ℎ=1ℎ = ℎ120573ℎ(119877119894)) (119888 minus 1)
Pseudocode 1 Pseudocode for calculating grade of certainty CF for 119877119894
not care The grade of certainty (CF) for each fuzzy rule isdetermined by (Pseudocode 1) Compatibility (120583) of a pat-tern to a rule is the product of membership amount of pat-tern at each dimension Zero compatibility of a pattern to arule means that the rule has not covered the pattern Aftercalculating 120583 for each pattern the relative sum of compatibil-ities (120573) is calculated per class and finally the certainty factoris achieved by relative difference of maximum value of 120573 andsum of other 120573s
42 Fuzzy Reasoning When the antecedent fuzzy sets of eachrule are given we can determine consequent class and thegrade of certainty of each rule by fuzzy rule generationmethod which has been described in previous section indetail The proposed classifier in this paper generates a setof fuzzy if-rules The achieved rule set is then employed topredict unknown instances The fuzzy reasoning procedureensures us which rules can vote for class of the test instanceWe use single winner rule in our algorithm Let us assumethat we have a set of fuzzy rules 119878 extracted from training dataset The input pattern 119884119901 = (1199101199011 1199101199012 119910119901119899) is classified bya single winner rule 119877119872 in 119878 which is determined as follows
Product of compatibility grade of input test instance andgrade of certainty for thewinner rule has themost value in therule set
5 Research Procedure
This section presents the proposed algorithm and discussesabout each of its steps in detail Comprehensible creditscoring-FAIS (CCS-FAIS) [31] and fuzzy artificial immunesystem (FAIS) [30] are two fuzzy classifiers that we haveproposed earlier using immune principles These classifierswere based on the clonal selection theoryThe clonal selectionprinciple is used to describe the main features of an adaptiveimmune response to an antigenic stimulus The main idea isthat only those B cells that identify the antigens are selected toproliferate The selected cells are exposed to an affinity mat-uration process which develops their affinity to the select-ive antigens In this paper no distinction is made between a Bcell and its antibody therefore each individual in our im-mune model will be called B cell
Our previous FAIS and CCS-FAIS classification systemsused population of B cells In these classifiers each B cell had
primary age to live in the population Age of B cells shouldbe increased if their fitness had been improved during thematuration process otherwise those B cells that their currentages reach to their corresponding maximum age thresholdswould die
In this paper we have improved the performance of FAISand CCS-FAIS classifiers The differences of IFAIS (currentpaper method) with CCS-FAIS and FAIS are as follows
(1) In our proposed model we have employed immunememory to remember good B cells during the cloningprocess
(2) We have designed two forms ofmemory to remembergood B cells during the cloning process simple mem-ory and 119896-layer memory
(3) The IFAIS benefits from using several diverse selec-tion procedures to develop an efficient clonal selec-tion algorithm
The goal of the immune model is to obtain a set of ruleswith high accuracy Each B cell represents a rule As we men-tioned in Section 3 each rule is coded according to Figure 1
51 Affinity Functions Equation (4) demonstrates the usedaffinity functions which have been previously presented inCCS-FAIS and FAIS [30 31] Consider
52 Immune Memory The memory cells in natural immunesystem are used for eliminating similar foreign substances Inthis paper we have employed immune memory during thecloning process for selected B cells According to the cloning
Advances in Fuzzy Systems 5
procedure IFAIS
beginInitialization() a population of B cells is generatedRule Generation() a population of B cells searches for optimized rule iterativelyRule Learning() From the final population the best B cell based on fitness is selectedTermination Test If a stopping condition is satisfied the learning of current class is finished andthe algorithm is going to learn the next class
End
Pseudocode 2 Pseudocode of IFAIS
(1) procedure Proposed Classifier(2) do(3) Set current learning class as 119888(4) While Termination Test(5) Generate initial B-cell repertoire from class c antigens(6) While cycle ltMax Iterations (7) Perform Clonal Selection Procedure(8) Use three selection procedures as(9) (1) Roulette Wheel Selection(10) (2) Tournament Selection(11) (3) Uniform Selection(12) Usememory (Simple and k-layered to clone selected B-Cells(13) PerformHyper-mutation(14)
(15) Perform Rule Learning Procedure(16) (1) Select the best B cell(17) (2) Add rule of the best B cell to the current rule set(18) If classification rate is not increased then the current loop exits(19)
(20) Until All classes have been learned
Algorithm 1 An overview of the proposed classifier At initialization a population of B-cells is generated from instances of class 119888 thensome B-cells are selected to proliferate in rule generation phase The life cycle of B-cells is controlled by age The best B-cell is added to ruleset if the classification rate increases more than a threshold At last if the termination test satisfies the classifier learns rules for class 119888
method a B cell is changed randomly Randomness of themodification is a way of exploring in the search space Thebalance of exploration and exploitation is a major problem inheuristic search algorithms In order to exploit the previousknowledge of cloning the memory records the changes of Bcells which enables the algorithm to produce higher quality BcellsThe cloningmethodwith this kind ofmemory increasesthe probability ofmodifications which have been recorded inmemory in former iterations of algorithmWe called this typeof memory simple memory In each iteration the contentsof memory degrade slightly The effectiveness of memorydecreases gradually using the proliferation procedure Whenthe generation of high quality B cells using the memoryis stopped the number of biased memory-based changesdecreases accordingly
During the cloning process it might be more effectiveif we consider more than one modification for the selectedB cell In a simple memory all changes are recorded inde-pendently therefore we define a new type of memory whichis named k-layer memory In this memory type 119896 is themaximum number of simultaneous changes on a B cell For
example a 3-layer memory contains 3 kinds of memoriesThe first memory records just 1 modification the secondmemory records 2 simultaneous modifications and the lastmemory records 3 simultaneous modifications A 119896-layermemory needs a large amount of physical memory to runefficiently therefore it is not a useful method for huge datasetsThedetailed implementation of thesememories has beenexplained in the next section
53 Proposed Classifier An overview of the proposed classi-fier is presented in Pseudocode 2 and Algorithm 1The mainloop of the algorithm applies the learning procedure for eachclass separately This loop consists of 4 steps initializationrule generation rule learning and termination test Rulegeneration phase employs an AIS-based algorithm to finda single rule based on the initiated population In the rulelearning stage when a rule is added to the final learnedrule set the learning mechanism reduces the weight of thosetraining instances that are covered by the new learned ruleTherefore in the next rule generation round the AIS-based
6 Advances in Fuzzy Systems
rule induction procedure focuses on those instances that arecurrently uncovered or misclassified At the beginning of thelearning process the weights of the whole training instancesare set to 1 Each step of the new proposed AIS-based algo-rithm is described briefly in Pseudocode 2 The details ofour algorithm is presented in Algorithm 1 (IFAIS stands forimproved FAIS)
(1) Initialization In this stage a population of B cells isgenerated The number of initial population is constant Thisnumber is a parameter which is named initial Population SizeTo generate a B cell an instance of current class from dataset is selected randomly and fuzzy terms for antecedent partof the rule (B cell) are computed according to each attributevalue of the selected training instance Consequent part of thegenerated rule becomes the class of selected instance Initialage of B cell is another parameter denoted by default AgeAfter generation of initial population fitness is computed foreach B cell independently
(2) Rule Generation In this step a population of B cellssearches for optimized rule iteratively At the first step ofIFAIS some B cells are selected to be cloned This selec-tion is based on roulette-wheel selection algorithm B cellswith higher fitness have more chance to be selected Thenumber of selected B cells is constant (selection Size) Nowit is time to proliferate the selected B cells Hypermutationoccurred during the cloning process A B cell contains arule and the rule has antecedents Hypermutation considersa change to these antecedents which causes a change to thecorresponding B cell Maximum number of simultaneouschanges in antecedents of a B cell would be determined by aparameter which is named max Term Changes Number Weneed to restrict the number of changes because increasingthe number of modified antecedents of a rule increases theprobability of corruption of that rule significantly Now arandom number is generated to determine the number ofchanges to the selected B cell (max value is max TermChanges Number) after that the algorithm determines whichantecedents must be changed using immune memory In thisalgorithm simple memory is presented by a matrix Rowsare fuzzy terms columns are attributes and entry (119894 119895) isthe value of changing jth attribute to 119894th fuzzy term so theprobability of choosing jth attribute is sum of jth columnentries divided by sum of all entries and the probability ofchanging to a fuzzy term is proportional to the value of eachfuzzy termThe determination of correct factor which wouldbe able to reveal the progress of a change is critical In thisalgorithm we use relative affinity (difference of new affinityand old affinity) as value of a change to a fuzzy term If thealgorithm uses 119896-layer memory we should note that 119896 is thesame as max Term Changes Number The 119896-layer memorycontains 119896 matrices Dimension of 1-matrix is like simplememory 119901-matrix is used when 119901 simultaneous changesoccurred therefore the number of columnswould be equal tothe number of attributes or 119862 (attributes 119901) and the numberof rows would be the same as num of fuzzy terms119901 If wedo not use memory the probability of changing an attributevalue to do not care is a parameter that is called dont Care
Replacement Rate The effect of memory controls by weightmeans of default probability and memory probability Thisweight is a parameter which is called memory Weight Num-ber of clones produced for each B cell is another parameterwhich is called clone Number The age of generated B cellsis calculated using (5) This equation controls the populationsize Consider
Agenew = Ageold + Agedefault times affinity
if affinitynew gt affinityold(5)
After cloning B cells of previous generations becameolder Some B cells would be deleted from the main popu-lation because their age reaches 0
(3) Rule Learning When AIS algorithm is finished the fittestB cell is selected The rule which is represented by this B cellis added to the final resulted rule set Then the classificationrate of current rule set is compared to the old rule set whichdoes not contain the new rule Classification rate is calculatedusing (6) If the difference is higher than a threshold (accuracyThreshold) the addition is accepted Consider
classification rate = NCPnumber of patterns
(6)
(4) Termination Test If a stopping condition is satisfied thelearning of current class is finished and the algorithm is goingto learn the next class If the condition is not satisfied thealgorithm tries to learn another rule by initializing a newpopulation for the next execution of AIS We can use anystopping condition for terminating the loop We limit thenumber of learned rules for each class This is done by aparameter which is calledmax Rule Set Size
54 Classification Reasoning Technique After rule extractionprocedure the classifier must employ these learned rulesto predict the class of a test record The usual reasoningmethod of fuzzy classifiers is based on (3) which is explainedin Section 4 in detail We use (3) to predict the class ofan input test instance whenever all of the rules are notapplicable for the input test instance The algorithm finds themost similar rule to this instance In this method a rule iscreated from the instance like the initialization phase primaryrules are generated from instances The most similar rule isthe rule which has the highest length of longest commonsubsequence (LCS) with the newly generated ruleThe lengthof common subsequence of the selected rule must be greaterthanminimum lengthThis value is another parameter whichis named min Rule Similarity Length This method decreasesthe number of unclassified instances of the algorithm
6 Experimental Results
In this section two credit data sets were used to evaluatethe predictive accuracy of the proposed classifier Australiancredit approval and German credit approval data sets areavailable from UCI Machine Learning Repository In Aus-tralian credit approval data set all names and values have
Advances in Fuzzy Systems 7
Table 1 UCI datasets used in our experiments Instances of theAustralian are almost equally distributed between classes but in theGerman they are more unbalanced
Dataset Number ofclasses
Number ofattributes
Number ofinstances Classes
Australian 2 14 690 307 negative383 positive
German 2 24 1000 700 negative300 positive
Table 2 Parameter specification of IFAIS in our experiments
Parameter Value in Australian Value in Germaninitial Population Size 100 300max Iteration 50 50default Age 5 5selection Size 100 100clone Number 10 10max Term Changes Number 3 2dontCare Replacement Rate 05 02max Rule Set Size 5 10accuracy Threshold 003 003max Rule Similarity Length 10 17min Covered Percent 0 30memory Weight 05 05119908119875 001 035119908NCP 069 01119908119873 001 045119908NMP 029 01119908BF 08 0999119908LEN 02 0001
been changed to meaningless to protect confidentiality of thedata Table 1 illustrates the information of these data setsIn Australian credit data there are 383 instances where as-signing credit to them has high risk and 307 instances arecreditworthy applicants The German credit data is more un-balanced and it consists of 300 instances where creditshould not be assigned and 700 instances are creditworthyapplicants
Each value in the Australian and German data setsis normalized between 00 and 10 using the min-maxtransformation method Table 2 represents the parametersettings that have been used in IFAIS Simulations havebeen performed by Weka data mining tool Table 2 shows aninteresting fact about the used datasets the German creditscoring dataset is more complicated than Australian creditscoring dataset This is because of the need of IFAIS to workwith a greater initial population size and maximum rule setsize when it is applied on the German credit scoring dataset
In Figures 2 and 3 the progress of classification rate perrule of the proposed classifier for Australian and Germancredit data sets has been illustrated respectivelyThese figuresillustrate the role of each evolved fuzzy if-then rule for the twoused datasets Our algorithm uses iterative rule learning andit employs AIS per iteration to find a rule (rule generation
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule
Figure 2 Progress of classification rate per rule of IFAIS forAustralian credit data set
100
90
80
70
60
50
40
30
20
10
0
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Figure 3 Progress of classification rate per rule of IFAIS forGermancredit data set
phase) After the extraction of each rule the weights ofinstances that have been covered by the rule are decreased InIFAIS the instances are removed from data set which meansthe weights are set to zero According to Figures 2 and 3 thefirst extracted rules are more general and shorter than laterrules All of the extracted rules participate in the decision-making process and the rules classify almost the whole testdata
According to Figures 2 and 3 we can also compare thecomplexity of data sets To accomplish this we have extracted5 rules for each class of Australian dataset For each class ofthe German dataset we had 12 and 17 rules for negative andpositive classes respectively
The difference in number of extracted rules shows thatGerman data set patterns are more complex than Australian
8 Advances in Fuzzy Systems
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
algorithmWithin the proposed AIS fuzzy logic has been ap-plied to extract interpretable fuzzy rules [30 31]
Themain reason that encouraged us to use the AIS meta-heuristic for credit risk prediction problem is that AIS has anature which we can use it for our problem effectively Thisnature is that AIS tends to explore the search space of theproblem very efficientlyThis capability is associated with thehypermutation operator of AIS We have selected AIS forcredit scoring prediction problem because previous investi-gations show that the so-called classification problem has avery explorative search space We have experienced thisnature of credit scoring classification problem in our experi-ments vividly The main observation which shows the explo-rative nature of this problem is that the fitness function out-puts changes drastically for very similar inputs MoreoverAIS has proved its high performance for two-class classifica-tion problems in previous investigations
The new proposed classification system in this paper is animproved version of fuzzy artificial immune system (FAIS)[30] and comprehensible credit scoring- FAIS (CCS-FAIS)[31] classifiers as the two previous versions of AIS-based clas-sification system for credit risk prediction In our proposedmodel we have employed immune memory to remembergood B-cells during the cloning process We have designedtwo forms of memory simple memory and 119896-layer memoryResults demonstrate that our new definition of memory forAIS-based fuzzy rule extraction increases the final classifi-cation rate of credit scoring process considerably The WekaDataMining tool [32] has been used to compare our classifierwith several well-known classifiers
The rest of this paper is organized as follows Section 2discusses some algorithms presented for credit risk predic-tion problem In Section 3 we describe immune systemsand the concepts we have used in our proposed algorithmSection 4 describes pattern classificationwith fuzzy logicTheproposed algorithm is presented in Section 5 Section 6 pro-vides information of performed experiments and achievedresults Finally Section 7 concludes the paper
2 Literature Review
SVM is one of the popular learning methods presented forcredit scoring classification problem Choosing the optimalinput feature subset and setting the best kernel parameters arethe two problems that should be solved to propose an efficientSVM-based classifier [33] Zhang et al [3] and Huang et al[33] used SVM for credit scoring They show that SVM has ahigh and acceptable accuracy for this classification problem
Hybrid data mining approaches also have been proposedfor effective credit scoring Yao [34] used neighborhoodrough set and SVM as a hybrid classifier In this classifier aneighborhood rough set has been employed for feature selec-tion Zhang et al [35] proposed hybridmodel based on genet-ic programming (GP) and SVM This model used GP to ex-tract if-then rules and for remaining instances of dataset itemployed discriminator based on SVM Yi [36] used a com-bination of decision tree and simulated annealingmethods tobuild a model In this hybridization authors have combined
local search strategy of decision tree algorithms and globaloptimization of simulated annealing algorithm
Exploring new techniques in credit scoring performanceimprovement can save too much money In recent yearsmany bioinspired algorithms are presented for solving clas-sification problems such as credit card fraud detection [37]credit scoring security and other applications [38] Amongthese approaches AIS is one of the newest methods that hasbeen applied for the credit scoring purposes Leung et al [9]proposed a simple AIS (SAIS) algorithm that adopted few keyconcepts of AIS (affinity measure cloning and mutation)They found SAIS a very competitive classifier
Fuzzy logic has been used for designing classificationsystems drastically [39 40]The important advantage of fuzzylogic is its influential capability in managing uncertainty andvagueness [41]Most of fuzzy classifiers generate a list of fuzzyif-then rules These rules are represented in linguistic formsthat make them interpretable by users Experts can validateand correct the rules This increases the interaction withusers Lei and Ren-hou [42] proposed a classifier based onimmune principles and fuzzy rules They apply their algo-rithm on 15 well-known UCI machine learning repository[43] data sets and achieve high accuracy The fuzzy AIS termin our proposed method is similar to Lei and Ren-houmethodThemajor difference between our proposedmethodand Lei and Ren-hou algorithm is in the definition of fitnessfunctionThey used a simple function as fitness function butwe have improved fitness function by extra terms This func-tion has been discussed in Section 5 in detail
3 Immune Systems
Researchers have been inspired by biology in solving com-putational problems There have been several techniques onbiologicalmetaphors such as evolutionary algorithms swarmintelligence and neural networks [29] Artificial immune sys-tems are bioinspired algorithms that have been active andprolific over the last decade [44 45] The basis of AIS is hu-man immune system which exploits learning and memoriz-ing capabilities of immune systems [46] Timmis et al pro-posed the relation of immunology and computation [29] atthe 80sHunt andCooke investigated the nature of learning inthe immune system and proposed a learning algorithm [27]Timmis and Knight [28] de Castro and von Zuben [47] andDasgupta [48] developed basic models of artificial immunesystems which are the sources of current AIS algorithms Im-mune-inspired models have been applied on wide variety ofresearch fields ranging frompattern recognition such as clas-sification and clustering anomaly detection [49 50] and op-timization [51 52] to robotics [53 54] and image processing[55 56] The key characteristics of immune systems arelearning adaptability memory mechanisms and self-organ-ization which are desirable to inspired algorithms Clonal se-lection immune networks and negative selection are thethree main immunological theories that are employed asstrongly accepted perspectives in AIS
Advances in Fuzzy Systems 3
Class is cAttribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5 Attribute n
S DC L DC DC ML
rArr
Figure 1 A sample fuzzy rule which is ldquoif Attribute 1 is Small and Attribute 3 is Large and Attribute 119899 is Medium Large then class is 119888rdquo
31 Natural Immune System The human immune system is adistributed pattern detection system with many functionalcomponents located in specific parts throughout the bodyThe immune system controls defense mechanism throughinnate and adaptive responses [57] Innate responses areagainst any invaders that enter the body but adaptive re-sponses are directed against particular invaders and demon-strate learning recognition memory acquisition and self-regulations of the body These invaders that infect the bodyare called antigens Antigens provoke the immune responsesThe core of adaptive responses is lymphocytes which are pro-vided with a sort of receptors to recognize antigens Lympho-cytes are divided into two types as B cells and T cells In thecase of invasion appropriate B cells attempt to clonewith pro-ducing sufficient proteins to remove antigens (called antibod-ies) A B cell holds antibodies on its shell which can identifythe antigens invading the body The matching between anti-gen and antibody is complementary and is similar to ldquolockand keyrdquo [58] T cells do not interact with antigens directlyThey circulate through the body and scan the surface of bodycells for the presence of foreign antigens that have been com-bined with the cell Then T cells bind to these cells and be-come activated Activated T cells secrete some chemicals asalert signals to others B cells which take these signals fromthe T cells become stimulated with the detection of antigenby their antibodies
32 Clonal Selection Theory The clonal selection theorydescribes the basic response of the adaptive immune systemto an antigenic stimulus The idea is that only those cellsthat are capable of detecting the antigen will proliferate andothers cannot clone This theory applies for both T cells andB cells Before the receptor of B cells binds to an antigen andB cells become stimulated and differentiate into memorycells colonies of B cells are created During the cloning pro-cess B cells undergo somatic hypermutation which keepsthe diversity of B cell population for future strange antigensAfter cloning activated B cells (or memory cells) producehuge amounts of antibodies which results in elimination ofthe antigen Some of memory cells remain within the host togenerate a rapid response upon a subsequent encounter withthe same or similar antigen [29] CLONALG [59] and B cellalgorithm [60] are AIS algorithms which are based on clonalselection theory These algorithms have cloning mutationand selection operators which makes them similar to geneticalgorithms
4 Fuzzy Rule-Based Pattern Classification
In this section we briefly explain the fuzzy rule-based patternclassification method which was first proposed by Ishibuchi
et al [61] and used in many investigations [30 31 42 62ndash65] This method consists of fuzzy rule generation and fuzzyreasoning procedures
41 Fuzzy Rule Generation Let us assume that the patternspace is 119899-dimension continuous space with 119888 classes Forsimplicity each dimension must be in the unit interval [0 1]The training data set includes 119898 labeled patterns which isshown in
119883119901 = (1199091199011 1199091199012 119909119901119899) class is 119888119870
119901 = 1 2 119898 119870 = 1 2 119888
(1)
The purpose is generating fuzzy if-then rules with the fol-lowing form Rule 119877119894 if 1199091199011 is 119860 1198941 and and 119909119901119899 is 119860 119894119899then 119883119901 belongs to Class 119862119894 with CF = CF119894 where 119877119894 is thelabel of the 119894th fuzzy if-then rule 119860 1198941 119860119894119899 are antecedentfuzzy sets in the unit interval [0 1] 119862119894 is the resultant classand CF119894 is the certainty factor (or rule weight) of the fuzzy if-then rule 119877119894 which is a real number in the unit interval [0 1](Figure 1 demonstrates a sample fuzzy if-then rule) Theremight have been some do not care antecedents in the rules andthese antecedents are usually omittedTherefore the numberof antecedents of a rule is less than or equal to 119899 Some rulesmay have a few antecedent conditions which makes themmore understandable to users
We have used a typical set of linguistic values as ante-cedent fuzzy sets The membership function of each lin-guistic value is obtained by homogeneously partitioning thedomain of each attribute into symmetric triangular fuzzy sets(119891membership in (2))We use such simple specification in exper-iments to demonstrate the high performance of our fuzzyclassifier system even if the membership function of eachantecedent fuzzy set is not tailored However we can use anytailored membership function in our fuzzy classifier systemfor a particular pattern classification problem Consider
119891membership (119909) =
minus4119909 + 1 0 le 119909 lt 0125 997904rArr S4119909 0125 le 119909 lt 025 997904rArr MSminus4119909 + 2 025 le 119909 lt 0375 997904rArr MS4119909 minus 1 0375 le 119909 lt 05 997904rArr Mminus4119909 + 3 05 le 119909 lt 0625 997904rArr M4119909 minus 2 0625 le 119909 lt 075 997904rArr MLminus4119909 + 4 075 le 119909 lt 0875 997904rArr ML4119909 minus 3 0875 le 119909 le 1 997904rArr L
119891membership (DC) = 1 forall119909 isin [0 1]
(2)
where S MS M ML L and DC respectively stand forsmall medium small medium medium large large and do
4 Advances in Fuzzy Systems
Step 1 for each pattern119883119901 do(11) Compatibility 120583119894(119883119901) = prod
119899
119895=1119891membership(119909119901119895)
Step 2 for each class ℎ do(21) Calculate relative sum of compatibility grades 120573ℎ(119877119894) = (sum
Step 3 Find class ℎ which has maximum 120573ℎ (119877119894)Step 4 119862119865119894 = (120573
ℎ(119877119894) minus 120573)(sum
119888
ℎ=1120573ℎ(119877119894)) where 120573 = (sum
119888
ℎ=1ℎ = ℎ120573ℎ(119877119894)) (119888 minus 1)
Pseudocode 1 Pseudocode for calculating grade of certainty CF for 119877119894
not care The grade of certainty (CF) for each fuzzy rule isdetermined by (Pseudocode 1) Compatibility (120583) of a pat-tern to a rule is the product of membership amount of pat-tern at each dimension Zero compatibility of a pattern to arule means that the rule has not covered the pattern Aftercalculating 120583 for each pattern the relative sum of compatibil-ities (120573) is calculated per class and finally the certainty factoris achieved by relative difference of maximum value of 120573 andsum of other 120573s
42 Fuzzy Reasoning When the antecedent fuzzy sets of eachrule are given we can determine consequent class and thegrade of certainty of each rule by fuzzy rule generationmethod which has been described in previous section indetail The proposed classifier in this paper generates a setof fuzzy if-rules The achieved rule set is then employed topredict unknown instances The fuzzy reasoning procedureensures us which rules can vote for class of the test instanceWe use single winner rule in our algorithm Let us assumethat we have a set of fuzzy rules 119878 extracted from training dataset The input pattern 119884119901 = (1199101199011 1199101199012 119910119901119899) is classified bya single winner rule 119877119872 in 119878 which is determined as follows
Product of compatibility grade of input test instance andgrade of certainty for thewinner rule has themost value in therule set
5 Research Procedure
This section presents the proposed algorithm and discussesabout each of its steps in detail Comprehensible creditscoring-FAIS (CCS-FAIS) [31] and fuzzy artificial immunesystem (FAIS) [30] are two fuzzy classifiers that we haveproposed earlier using immune principles These classifierswere based on the clonal selection theoryThe clonal selectionprinciple is used to describe the main features of an adaptiveimmune response to an antigenic stimulus The main idea isthat only those B cells that identify the antigens are selected toproliferate The selected cells are exposed to an affinity mat-uration process which develops their affinity to the select-ive antigens In this paper no distinction is made between a Bcell and its antibody therefore each individual in our im-mune model will be called B cell
Our previous FAIS and CCS-FAIS classification systemsused population of B cells In these classifiers each B cell had
primary age to live in the population Age of B cells shouldbe increased if their fitness had been improved during thematuration process otherwise those B cells that their currentages reach to their corresponding maximum age thresholdswould die
In this paper we have improved the performance of FAISand CCS-FAIS classifiers The differences of IFAIS (currentpaper method) with CCS-FAIS and FAIS are as follows
(1) In our proposed model we have employed immunememory to remember good B cells during the cloningprocess
(2) We have designed two forms ofmemory to remembergood B cells during the cloning process simple mem-ory and 119896-layer memory
(3) The IFAIS benefits from using several diverse selec-tion procedures to develop an efficient clonal selec-tion algorithm
The goal of the immune model is to obtain a set of ruleswith high accuracy Each B cell represents a rule As we men-tioned in Section 3 each rule is coded according to Figure 1
51 Affinity Functions Equation (4) demonstrates the usedaffinity functions which have been previously presented inCCS-FAIS and FAIS [30 31] Consider
52 Immune Memory The memory cells in natural immunesystem are used for eliminating similar foreign substances Inthis paper we have employed immune memory during thecloning process for selected B cells According to the cloning
Advances in Fuzzy Systems 5
procedure IFAIS
beginInitialization() a population of B cells is generatedRule Generation() a population of B cells searches for optimized rule iterativelyRule Learning() From the final population the best B cell based on fitness is selectedTermination Test If a stopping condition is satisfied the learning of current class is finished andthe algorithm is going to learn the next class
End
Pseudocode 2 Pseudocode of IFAIS
(1) procedure Proposed Classifier(2) do(3) Set current learning class as 119888(4) While Termination Test(5) Generate initial B-cell repertoire from class c antigens(6) While cycle ltMax Iterations (7) Perform Clonal Selection Procedure(8) Use three selection procedures as(9) (1) Roulette Wheel Selection(10) (2) Tournament Selection(11) (3) Uniform Selection(12) Usememory (Simple and k-layered to clone selected B-Cells(13) PerformHyper-mutation(14)
(15) Perform Rule Learning Procedure(16) (1) Select the best B cell(17) (2) Add rule of the best B cell to the current rule set(18) If classification rate is not increased then the current loop exits(19)
(20) Until All classes have been learned
Algorithm 1 An overview of the proposed classifier At initialization a population of B-cells is generated from instances of class 119888 thensome B-cells are selected to proliferate in rule generation phase The life cycle of B-cells is controlled by age The best B-cell is added to ruleset if the classification rate increases more than a threshold At last if the termination test satisfies the classifier learns rules for class 119888
method a B cell is changed randomly Randomness of themodification is a way of exploring in the search space Thebalance of exploration and exploitation is a major problem inheuristic search algorithms In order to exploit the previousknowledge of cloning the memory records the changes of Bcells which enables the algorithm to produce higher quality BcellsThe cloningmethodwith this kind ofmemory increasesthe probability ofmodifications which have been recorded inmemory in former iterations of algorithmWe called this typeof memory simple memory In each iteration the contentsof memory degrade slightly The effectiveness of memorydecreases gradually using the proliferation procedure Whenthe generation of high quality B cells using the memoryis stopped the number of biased memory-based changesdecreases accordingly
During the cloning process it might be more effectiveif we consider more than one modification for the selectedB cell In a simple memory all changes are recorded inde-pendently therefore we define a new type of memory whichis named k-layer memory In this memory type 119896 is themaximum number of simultaneous changes on a B cell For
example a 3-layer memory contains 3 kinds of memoriesThe first memory records just 1 modification the secondmemory records 2 simultaneous modifications and the lastmemory records 3 simultaneous modifications A 119896-layermemory needs a large amount of physical memory to runefficiently therefore it is not a useful method for huge datasetsThedetailed implementation of thesememories has beenexplained in the next section
53 Proposed Classifier An overview of the proposed classi-fier is presented in Pseudocode 2 and Algorithm 1The mainloop of the algorithm applies the learning procedure for eachclass separately This loop consists of 4 steps initializationrule generation rule learning and termination test Rulegeneration phase employs an AIS-based algorithm to finda single rule based on the initiated population In the rulelearning stage when a rule is added to the final learnedrule set the learning mechanism reduces the weight of thosetraining instances that are covered by the new learned ruleTherefore in the next rule generation round the AIS-based
6 Advances in Fuzzy Systems
rule induction procedure focuses on those instances that arecurrently uncovered or misclassified At the beginning of thelearning process the weights of the whole training instancesare set to 1 Each step of the new proposed AIS-based algo-rithm is described briefly in Pseudocode 2 The details ofour algorithm is presented in Algorithm 1 (IFAIS stands forimproved FAIS)
(1) Initialization In this stage a population of B cells isgenerated The number of initial population is constant Thisnumber is a parameter which is named initial Population SizeTo generate a B cell an instance of current class from dataset is selected randomly and fuzzy terms for antecedent partof the rule (B cell) are computed according to each attributevalue of the selected training instance Consequent part of thegenerated rule becomes the class of selected instance Initialage of B cell is another parameter denoted by default AgeAfter generation of initial population fitness is computed foreach B cell independently
(2) Rule Generation In this step a population of B cellssearches for optimized rule iteratively At the first step ofIFAIS some B cells are selected to be cloned This selec-tion is based on roulette-wheel selection algorithm B cellswith higher fitness have more chance to be selected Thenumber of selected B cells is constant (selection Size) Nowit is time to proliferate the selected B cells Hypermutationoccurred during the cloning process A B cell contains arule and the rule has antecedents Hypermutation considersa change to these antecedents which causes a change to thecorresponding B cell Maximum number of simultaneouschanges in antecedents of a B cell would be determined by aparameter which is named max Term Changes Number Weneed to restrict the number of changes because increasingthe number of modified antecedents of a rule increases theprobability of corruption of that rule significantly Now arandom number is generated to determine the number ofchanges to the selected B cell (max value is max TermChanges Number) after that the algorithm determines whichantecedents must be changed using immune memory In thisalgorithm simple memory is presented by a matrix Rowsare fuzzy terms columns are attributes and entry (119894 119895) isthe value of changing jth attribute to 119894th fuzzy term so theprobability of choosing jth attribute is sum of jth columnentries divided by sum of all entries and the probability ofchanging to a fuzzy term is proportional to the value of eachfuzzy termThe determination of correct factor which wouldbe able to reveal the progress of a change is critical In thisalgorithm we use relative affinity (difference of new affinityand old affinity) as value of a change to a fuzzy term If thealgorithm uses 119896-layer memory we should note that 119896 is thesame as max Term Changes Number The 119896-layer memorycontains 119896 matrices Dimension of 1-matrix is like simplememory 119901-matrix is used when 119901 simultaneous changesoccurred therefore the number of columnswould be equal tothe number of attributes or 119862 (attributes 119901) and the numberof rows would be the same as num of fuzzy terms119901 If wedo not use memory the probability of changing an attributevalue to do not care is a parameter that is called dont Care
Replacement Rate The effect of memory controls by weightmeans of default probability and memory probability Thisweight is a parameter which is called memory Weight Num-ber of clones produced for each B cell is another parameterwhich is called clone Number The age of generated B cellsis calculated using (5) This equation controls the populationsize Consider
Agenew = Ageold + Agedefault times affinity
if affinitynew gt affinityold(5)
After cloning B cells of previous generations becameolder Some B cells would be deleted from the main popu-lation because their age reaches 0
(3) Rule Learning When AIS algorithm is finished the fittestB cell is selected The rule which is represented by this B cellis added to the final resulted rule set Then the classificationrate of current rule set is compared to the old rule set whichdoes not contain the new rule Classification rate is calculatedusing (6) If the difference is higher than a threshold (accuracyThreshold) the addition is accepted Consider
classification rate = NCPnumber of patterns
(6)
(4) Termination Test If a stopping condition is satisfied thelearning of current class is finished and the algorithm is goingto learn the next class If the condition is not satisfied thealgorithm tries to learn another rule by initializing a newpopulation for the next execution of AIS We can use anystopping condition for terminating the loop We limit thenumber of learned rules for each class This is done by aparameter which is calledmax Rule Set Size
54 Classification Reasoning Technique After rule extractionprocedure the classifier must employ these learned rulesto predict the class of a test record The usual reasoningmethod of fuzzy classifiers is based on (3) which is explainedin Section 4 in detail We use (3) to predict the class ofan input test instance whenever all of the rules are notapplicable for the input test instance The algorithm finds themost similar rule to this instance In this method a rule iscreated from the instance like the initialization phase primaryrules are generated from instances The most similar rule isthe rule which has the highest length of longest commonsubsequence (LCS) with the newly generated ruleThe lengthof common subsequence of the selected rule must be greaterthanminimum lengthThis value is another parameter whichis named min Rule Similarity Length This method decreasesthe number of unclassified instances of the algorithm
6 Experimental Results
In this section two credit data sets were used to evaluatethe predictive accuracy of the proposed classifier Australiancredit approval and German credit approval data sets areavailable from UCI Machine Learning Repository In Aus-tralian credit approval data set all names and values have
Advances in Fuzzy Systems 7
Table 1 UCI datasets used in our experiments Instances of theAustralian are almost equally distributed between classes but in theGerman they are more unbalanced
Dataset Number ofclasses
Number ofattributes
Number ofinstances Classes
Australian 2 14 690 307 negative383 positive
German 2 24 1000 700 negative300 positive
Table 2 Parameter specification of IFAIS in our experiments
Parameter Value in Australian Value in Germaninitial Population Size 100 300max Iteration 50 50default Age 5 5selection Size 100 100clone Number 10 10max Term Changes Number 3 2dontCare Replacement Rate 05 02max Rule Set Size 5 10accuracy Threshold 003 003max Rule Similarity Length 10 17min Covered Percent 0 30memory Weight 05 05119908119875 001 035119908NCP 069 01119908119873 001 045119908NMP 029 01119908BF 08 0999119908LEN 02 0001
been changed to meaningless to protect confidentiality of thedata Table 1 illustrates the information of these data setsIn Australian credit data there are 383 instances where as-signing credit to them has high risk and 307 instances arecreditworthy applicants The German credit data is more un-balanced and it consists of 300 instances where creditshould not be assigned and 700 instances are creditworthyapplicants
Each value in the Australian and German data setsis normalized between 00 and 10 using the min-maxtransformation method Table 2 represents the parametersettings that have been used in IFAIS Simulations havebeen performed by Weka data mining tool Table 2 shows aninteresting fact about the used datasets the German creditscoring dataset is more complicated than Australian creditscoring dataset This is because of the need of IFAIS to workwith a greater initial population size and maximum rule setsize when it is applied on the German credit scoring dataset
In Figures 2 and 3 the progress of classification rate perrule of the proposed classifier for Australian and Germancredit data sets has been illustrated respectivelyThese figuresillustrate the role of each evolved fuzzy if-then rule for the twoused datasets Our algorithm uses iterative rule learning andit employs AIS per iteration to find a rule (rule generation
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule
Figure 2 Progress of classification rate per rule of IFAIS forAustralian credit data set
100
90
80
70
60
50
40
30
20
10
0
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Figure 3 Progress of classification rate per rule of IFAIS forGermancredit data set
phase) After the extraction of each rule the weights ofinstances that have been covered by the rule are decreased InIFAIS the instances are removed from data set which meansthe weights are set to zero According to Figures 2 and 3 thefirst extracted rules are more general and shorter than laterrules All of the extracted rules participate in the decision-making process and the rules classify almost the whole testdata
According to Figures 2 and 3 we can also compare thecomplexity of data sets To accomplish this we have extracted5 rules for each class of Australian dataset For each class ofthe German dataset we had 12 and 17 rules for negative andpositive classes respectively
The difference in number of extracted rules shows thatGerman data set patterns are more complex than Australian
8 Advances in Fuzzy Systems
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
Class is cAttribute 1 Attribute 2 Attribute 3 Attribute 4 Attribute 5 Attribute n
S DC L DC DC ML
rArr
Figure 1 A sample fuzzy rule which is ldquoif Attribute 1 is Small and Attribute 3 is Large and Attribute 119899 is Medium Large then class is 119888rdquo
31 Natural Immune System The human immune system is adistributed pattern detection system with many functionalcomponents located in specific parts throughout the bodyThe immune system controls defense mechanism throughinnate and adaptive responses [57] Innate responses areagainst any invaders that enter the body but adaptive re-sponses are directed against particular invaders and demon-strate learning recognition memory acquisition and self-regulations of the body These invaders that infect the bodyare called antigens Antigens provoke the immune responsesThe core of adaptive responses is lymphocytes which are pro-vided with a sort of receptors to recognize antigens Lympho-cytes are divided into two types as B cells and T cells In thecase of invasion appropriate B cells attempt to clonewith pro-ducing sufficient proteins to remove antigens (called antibod-ies) A B cell holds antibodies on its shell which can identifythe antigens invading the body The matching between anti-gen and antibody is complementary and is similar to ldquolockand keyrdquo [58] T cells do not interact with antigens directlyThey circulate through the body and scan the surface of bodycells for the presence of foreign antigens that have been com-bined with the cell Then T cells bind to these cells and be-come activated Activated T cells secrete some chemicals asalert signals to others B cells which take these signals fromthe T cells become stimulated with the detection of antigenby their antibodies
32 Clonal Selection Theory The clonal selection theorydescribes the basic response of the adaptive immune systemto an antigenic stimulus The idea is that only those cellsthat are capable of detecting the antigen will proliferate andothers cannot clone This theory applies for both T cells andB cells Before the receptor of B cells binds to an antigen andB cells become stimulated and differentiate into memorycells colonies of B cells are created During the cloning pro-cess B cells undergo somatic hypermutation which keepsthe diversity of B cell population for future strange antigensAfter cloning activated B cells (or memory cells) producehuge amounts of antibodies which results in elimination ofthe antigen Some of memory cells remain within the host togenerate a rapid response upon a subsequent encounter withthe same or similar antigen [29] CLONALG [59] and B cellalgorithm [60] are AIS algorithms which are based on clonalselection theory These algorithms have cloning mutationand selection operators which makes them similar to geneticalgorithms
4 Fuzzy Rule-Based Pattern Classification
In this section we briefly explain the fuzzy rule-based patternclassification method which was first proposed by Ishibuchi
et al [61] and used in many investigations [30 31 42 62ndash65] This method consists of fuzzy rule generation and fuzzyreasoning procedures
41 Fuzzy Rule Generation Let us assume that the patternspace is 119899-dimension continuous space with 119888 classes Forsimplicity each dimension must be in the unit interval [0 1]The training data set includes 119898 labeled patterns which isshown in
119883119901 = (1199091199011 1199091199012 119909119901119899) class is 119888119870
119901 = 1 2 119898 119870 = 1 2 119888
(1)
The purpose is generating fuzzy if-then rules with the fol-lowing form Rule 119877119894 if 1199091199011 is 119860 1198941 and and 119909119901119899 is 119860 119894119899then 119883119901 belongs to Class 119862119894 with CF = CF119894 where 119877119894 is thelabel of the 119894th fuzzy if-then rule 119860 1198941 119860119894119899 are antecedentfuzzy sets in the unit interval [0 1] 119862119894 is the resultant classand CF119894 is the certainty factor (or rule weight) of the fuzzy if-then rule 119877119894 which is a real number in the unit interval [0 1](Figure 1 demonstrates a sample fuzzy if-then rule) Theremight have been some do not care antecedents in the rules andthese antecedents are usually omittedTherefore the numberof antecedents of a rule is less than or equal to 119899 Some rulesmay have a few antecedent conditions which makes themmore understandable to users
We have used a typical set of linguistic values as ante-cedent fuzzy sets The membership function of each lin-guistic value is obtained by homogeneously partitioning thedomain of each attribute into symmetric triangular fuzzy sets(119891membership in (2))We use such simple specification in exper-iments to demonstrate the high performance of our fuzzyclassifier system even if the membership function of eachantecedent fuzzy set is not tailored However we can use anytailored membership function in our fuzzy classifier systemfor a particular pattern classification problem Consider
119891membership (119909) =
minus4119909 + 1 0 le 119909 lt 0125 997904rArr S4119909 0125 le 119909 lt 025 997904rArr MSminus4119909 + 2 025 le 119909 lt 0375 997904rArr MS4119909 minus 1 0375 le 119909 lt 05 997904rArr Mminus4119909 + 3 05 le 119909 lt 0625 997904rArr M4119909 minus 2 0625 le 119909 lt 075 997904rArr MLminus4119909 + 4 075 le 119909 lt 0875 997904rArr ML4119909 minus 3 0875 le 119909 le 1 997904rArr L
119891membership (DC) = 1 forall119909 isin [0 1]
(2)
where S MS M ML L and DC respectively stand forsmall medium small medium medium large large and do
4 Advances in Fuzzy Systems
Step 1 for each pattern119883119901 do(11) Compatibility 120583119894(119883119901) = prod
119899
119895=1119891membership(119909119901119895)
Step 2 for each class ℎ do(21) Calculate relative sum of compatibility grades 120573ℎ(119877119894) = (sum
Step 3 Find class ℎ which has maximum 120573ℎ (119877119894)Step 4 119862119865119894 = (120573
ℎ(119877119894) minus 120573)(sum
119888
ℎ=1120573ℎ(119877119894)) where 120573 = (sum
119888
ℎ=1ℎ = ℎ120573ℎ(119877119894)) (119888 minus 1)
Pseudocode 1 Pseudocode for calculating grade of certainty CF for 119877119894
not care The grade of certainty (CF) for each fuzzy rule isdetermined by (Pseudocode 1) Compatibility (120583) of a pat-tern to a rule is the product of membership amount of pat-tern at each dimension Zero compatibility of a pattern to arule means that the rule has not covered the pattern Aftercalculating 120583 for each pattern the relative sum of compatibil-ities (120573) is calculated per class and finally the certainty factoris achieved by relative difference of maximum value of 120573 andsum of other 120573s
42 Fuzzy Reasoning When the antecedent fuzzy sets of eachrule are given we can determine consequent class and thegrade of certainty of each rule by fuzzy rule generationmethod which has been described in previous section indetail The proposed classifier in this paper generates a setof fuzzy if-rules The achieved rule set is then employed topredict unknown instances The fuzzy reasoning procedureensures us which rules can vote for class of the test instanceWe use single winner rule in our algorithm Let us assumethat we have a set of fuzzy rules 119878 extracted from training dataset The input pattern 119884119901 = (1199101199011 1199101199012 119910119901119899) is classified bya single winner rule 119877119872 in 119878 which is determined as follows
Product of compatibility grade of input test instance andgrade of certainty for thewinner rule has themost value in therule set
5 Research Procedure
This section presents the proposed algorithm and discussesabout each of its steps in detail Comprehensible creditscoring-FAIS (CCS-FAIS) [31] and fuzzy artificial immunesystem (FAIS) [30] are two fuzzy classifiers that we haveproposed earlier using immune principles These classifierswere based on the clonal selection theoryThe clonal selectionprinciple is used to describe the main features of an adaptiveimmune response to an antigenic stimulus The main idea isthat only those B cells that identify the antigens are selected toproliferate The selected cells are exposed to an affinity mat-uration process which develops their affinity to the select-ive antigens In this paper no distinction is made between a Bcell and its antibody therefore each individual in our im-mune model will be called B cell
Our previous FAIS and CCS-FAIS classification systemsused population of B cells In these classifiers each B cell had
primary age to live in the population Age of B cells shouldbe increased if their fitness had been improved during thematuration process otherwise those B cells that their currentages reach to their corresponding maximum age thresholdswould die
In this paper we have improved the performance of FAISand CCS-FAIS classifiers The differences of IFAIS (currentpaper method) with CCS-FAIS and FAIS are as follows
(1) In our proposed model we have employed immunememory to remember good B cells during the cloningprocess
(2) We have designed two forms ofmemory to remembergood B cells during the cloning process simple mem-ory and 119896-layer memory
(3) The IFAIS benefits from using several diverse selec-tion procedures to develop an efficient clonal selec-tion algorithm
The goal of the immune model is to obtain a set of ruleswith high accuracy Each B cell represents a rule As we men-tioned in Section 3 each rule is coded according to Figure 1
51 Affinity Functions Equation (4) demonstrates the usedaffinity functions which have been previously presented inCCS-FAIS and FAIS [30 31] Consider
52 Immune Memory The memory cells in natural immunesystem are used for eliminating similar foreign substances Inthis paper we have employed immune memory during thecloning process for selected B cells According to the cloning
Advances in Fuzzy Systems 5
procedure IFAIS
beginInitialization() a population of B cells is generatedRule Generation() a population of B cells searches for optimized rule iterativelyRule Learning() From the final population the best B cell based on fitness is selectedTermination Test If a stopping condition is satisfied the learning of current class is finished andthe algorithm is going to learn the next class
End
Pseudocode 2 Pseudocode of IFAIS
(1) procedure Proposed Classifier(2) do(3) Set current learning class as 119888(4) While Termination Test(5) Generate initial B-cell repertoire from class c antigens(6) While cycle ltMax Iterations (7) Perform Clonal Selection Procedure(8) Use three selection procedures as(9) (1) Roulette Wheel Selection(10) (2) Tournament Selection(11) (3) Uniform Selection(12) Usememory (Simple and k-layered to clone selected B-Cells(13) PerformHyper-mutation(14)
(15) Perform Rule Learning Procedure(16) (1) Select the best B cell(17) (2) Add rule of the best B cell to the current rule set(18) If classification rate is not increased then the current loop exits(19)
(20) Until All classes have been learned
Algorithm 1 An overview of the proposed classifier At initialization a population of B-cells is generated from instances of class 119888 thensome B-cells are selected to proliferate in rule generation phase The life cycle of B-cells is controlled by age The best B-cell is added to ruleset if the classification rate increases more than a threshold At last if the termination test satisfies the classifier learns rules for class 119888
method a B cell is changed randomly Randomness of themodification is a way of exploring in the search space Thebalance of exploration and exploitation is a major problem inheuristic search algorithms In order to exploit the previousknowledge of cloning the memory records the changes of Bcells which enables the algorithm to produce higher quality BcellsThe cloningmethodwith this kind ofmemory increasesthe probability ofmodifications which have been recorded inmemory in former iterations of algorithmWe called this typeof memory simple memory In each iteration the contentsof memory degrade slightly The effectiveness of memorydecreases gradually using the proliferation procedure Whenthe generation of high quality B cells using the memoryis stopped the number of biased memory-based changesdecreases accordingly
During the cloning process it might be more effectiveif we consider more than one modification for the selectedB cell In a simple memory all changes are recorded inde-pendently therefore we define a new type of memory whichis named k-layer memory In this memory type 119896 is themaximum number of simultaneous changes on a B cell For
example a 3-layer memory contains 3 kinds of memoriesThe first memory records just 1 modification the secondmemory records 2 simultaneous modifications and the lastmemory records 3 simultaneous modifications A 119896-layermemory needs a large amount of physical memory to runefficiently therefore it is not a useful method for huge datasetsThedetailed implementation of thesememories has beenexplained in the next section
53 Proposed Classifier An overview of the proposed classi-fier is presented in Pseudocode 2 and Algorithm 1The mainloop of the algorithm applies the learning procedure for eachclass separately This loop consists of 4 steps initializationrule generation rule learning and termination test Rulegeneration phase employs an AIS-based algorithm to finda single rule based on the initiated population In the rulelearning stage when a rule is added to the final learnedrule set the learning mechanism reduces the weight of thosetraining instances that are covered by the new learned ruleTherefore in the next rule generation round the AIS-based
6 Advances in Fuzzy Systems
rule induction procedure focuses on those instances that arecurrently uncovered or misclassified At the beginning of thelearning process the weights of the whole training instancesare set to 1 Each step of the new proposed AIS-based algo-rithm is described briefly in Pseudocode 2 The details ofour algorithm is presented in Algorithm 1 (IFAIS stands forimproved FAIS)
(1) Initialization In this stage a population of B cells isgenerated The number of initial population is constant Thisnumber is a parameter which is named initial Population SizeTo generate a B cell an instance of current class from dataset is selected randomly and fuzzy terms for antecedent partof the rule (B cell) are computed according to each attributevalue of the selected training instance Consequent part of thegenerated rule becomes the class of selected instance Initialage of B cell is another parameter denoted by default AgeAfter generation of initial population fitness is computed foreach B cell independently
(2) Rule Generation In this step a population of B cellssearches for optimized rule iteratively At the first step ofIFAIS some B cells are selected to be cloned This selec-tion is based on roulette-wheel selection algorithm B cellswith higher fitness have more chance to be selected Thenumber of selected B cells is constant (selection Size) Nowit is time to proliferate the selected B cells Hypermutationoccurred during the cloning process A B cell contains arule and the rule has antecedents Hypermutation considersa change to these antecedents which causes a change to thecorresponding B cell Maximum number of simultaneouschanges in antecedents of a B cell would be determined by aparameter which is named max Term Changes Number Weneed to restrict the number of changes because increasingthe number of modified antecedents of a rule increases theprobability of corruption of that rule significantly Now arandom number is generated to determine the number ofchanges to the selected B cell (max value is max TermChanges Number) after that the algorithm determines whichantecedents must be changed using immune memory In thisalgorithm simple memory is presented by a matrix Rowsare fuzzy terms columns are attributes and entry (119894 119895) isthe value of changing jth attribute to 119894th fuzzy term so theprobability of choosing jth attribute is sum of jth columnentries divided by sum of all entries and the probability ofchanging to a fuzzy term is proportional to the value of eachfuzzy termThe determination of correct factor which wouldbe able to reveal the progress of a change is critical In thisalgorithm we use relative affinity (difference of new affinityand old affinity) as value of a change to a fuzzy term If thealgorithm uses 119896-layer memory we should note that 119896 is thesame as max Term Changes Number The 119896-layer memorycontains 119896 matrices Dimension of 1-matrix is like simplememory 119901-matrix is used when 119901 simultaneous changesoccurred therefore the number of columnswould be equal tothe number of attributes or 119862 (attributes 119901) and the numberof rows would be the same as num of fuzzy terms119901 If wedo not use memory the probability of changing an attributevalue to do not care is a parameter that is called dont Care
Replacement Rate The effect of memory controls by weightmeans of default probability and memory probability Thisweight is a parameter which is called memory Weight Num-ber of clones produced for each B cell is another parameterwhich is called clone Number The age of generated B cellsis calculated using (5) This equation controls the populationsize Consider
Agenew = Ageold + Agedefault times affinity
if affinitynew gt affinityold(5)
After cloning B cells of previous generations becameolder Some B cells would be deleted from the main popu-lation because their age reaches 0
(3) Rule Learning When AIS algorithm is finished the fittestB cell is selected The rule which is represented by this B cellis added to the final resulted rule set Then the classificationrate of current rule set is compared to the old rule set whichdoes not contain the new rule Classification rate is calculatedusing (6) If the difference is higher than a threshold (accuracyThreshold) the addition is accepted Consider
classification rate = NCPnumber of patterns
(6)
(4) Termination Test If a stopping condition is satisfied thelearning of current class is finished and the algorithm is goingto learn the next class If the condition is not satisfied thealgorithm tries to learn another rule by initializing a newpopulation for the next execution of AIS We can use anystopping condition for terminating the loop We limit thenumber of learned rules for each class This is done by aparameter which is calledmax Rule Set Size
54 Classification Reasoning Technique After rule extractionprocedure the classifier must employ these learned rulesto predict the class of a test record The usual reasoningmethod of fuzzy classifiers is based on (3) which is explainedin Section 4 in detail We use (3) to predict the class ofan input test instance whenever all of the rules are notapplicable for the input test instance The algorithm finds themost similar rule to this instance In this method a rule iscreated from the instance like the initialization phase primaryrules are generated from instances The most similar rule isthe rule which has the highest length of longest commonsubsequence (LCS) with the newly generated ruleThe lengthof common subsequence of the selected rule must be greaterthanminimum lengthThis value is another parameter whichis named min Rule Similarity Length This method decreasesthe number of unclassified instances of the algorithm
6 Experimental Results
In this section two credit data sets were used to evaluatethe predictive accuracy of the proposed classifier Australiancredit approval and German credit approval data sets areavailable from UCI Machine Learning Repository In Aus-tralian credit approval data set all names and values have
Advances in Fuzzy Systems 7
Table 1 UCI datasets used in our experiments Instances of theAustralian are almost equally distributed between classes but in theGerman they are more unbalanced
Dataset Number ofclasses
Number ofattributes
Number ofinstances Classes
Australian 2 14 690 307 negative383 positive
German 2 24 1000 700 negative300 positive
Table 2 Parameter specification of IFAIS in our experiments
Parameter Value in Australian Value in Germaninitial Population Size 100 300max Iteration 50 50default Age 5 5selection Size 100 100clone Number 10 10max Term Changes Number 3 2dontCare Replacement Rate 05 02max Rule Set Size 5 10accuracy Threshold 003 003max Rule Similarity Length 10 17min Covered Percent 0 30memory Weight 05 05119908119875 001 035119908NCP 069 01119908119873 001 045119908NMP 029 01119908BF 08 0999119908LEN 02 0001
been changed to meaningless to protect confidentiality of thedata Table 1 illustrates the information of these data setsIn Australian credit data there are 383 instances where as-signing credit to them has high risk and 307 instances arecreditworthy applicants The German credit data is more un-balanced and it consists of 300 instances where creditshould not be assigned and 700 instances are creditworthyapplicants
Each value in the Australian and German data setsis normalized between 00 and 10 using the min-maxtransformation method Table 2 represents the parametersettings that have been used in IFAIS Simulations havebeen performed by Weka data mining tool Table 2 shows aninteresting fact about the used datasets the German creditscoring dataset is more complicated than Australian creditscoring dataset This is because of the need of IFAIS to workwith a greater initial population size and maximum rule setsize when it is applied on the German credit scoring dataset
In Figures 2 and 3 the progress of classification rate perrule of the proposed classifier for Australian and Germancredit data sets has been illustrated respectivelyThese figuresillustrate the role of each evolved fuzzy if-then rule for the twoused datasets Our algorithm uses iterative rule learning andit employs AIS per iteration to find a rule (rule generation
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule
Figure 2 Progress of classification rate per rule of IFAIS forAustralian credit data set
100
90
80
70
60
50
40
30
20
10
0
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Figure 3 Progress of classification rate per rule of IFAIS forGermancredit data set
phase) After the extraction of each rule the weights ofinstances that have been covered by the rule are decreased InIFAIS the instances are removed from data set which meansthe weights are set to zero According to Figures 2 and 3 thefirst extracted rules are more general and shorter than laterrules All of the extracted rules participate in the decision-making process and the rules classify almost the whole testdata
According to Figures 2 and 3 we can also compare thecomplexity of data sets To accomplish this we have extracted5 rules for each class of Australian dataset For each class ofthe German dataset we had 12 and 17 rules for negative andpositive classes respectively
The difference in number of extracted rules shows thatGerman data set patterns are more complex than Australian
8 Advances in Fuzzy Systems
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
Step 3 Find class ℎ which has maximum 120573ℎ (119877119894)Step 4 119862119865119894 = (120573
ℎ(119877119894) minus 120573)(sum
119888
ℎ=1120573ℎ(119877119894)) where 120573 = (sum
119888
ℎ=1ℎ = ℎ120573ℎ(119877119894)) (119888 minus 1)
Pseudocode 1 Pseudocode for calculating grade of certainty CF for 119877119894
not care The grade of certainty (CF) for each fuzzy rule isdetermined by (Pseudocode 1) Compatibility (120583) of a pat-tern to a rule is the product of membership amount of pat-tern at each dimension Zero compatibility of a pattern to arule means that the rule has not covered the pattern Aftercalculating 120583 for each pattern the relative sum of compatibil-ities (120573) is calculated per class and finally the certainty factoris achieved by relative difference of maximum value of 120573 andsum of other 120573s
42 Fuzzy Reasoning When the antecedent fuzzy sets of eachrule are given we can determine consequent class and thegrade of certainty of each rule by fuzzy rule generationmethod which has been described in previous section indetail The proposed classifier in this paper generates a setof fuzzy if-rules The achieved rule set is then employed topredict unknown instances The fuzzy reasoning procedureensures us which rules can vote for class of the test instanceWe use single winner rule in our algorithm Let us assumethat we have a set of fuzzy rules 119878 extracted from training dataset The input pattern 119884119901 = (1199101199011 1199101199012 119910119901119899) is classified bya single winner rule 119877119872 in 119878 which is determined as follows
Product of compatibility grade of input test instance andgrade of certainty for thewinner rule has themost value in therule set
5 Research Procedure
This section presents the proposed algorithm and discussesabout each of its steps in detail Comprehensible creditscoring-FAIS (CCS-FAIS) [31] and fuzzy artificial immunesystem (FAIS) [30] are two fuzzy classifiers that we haveproposed earlier using immune principles These classifierswere based on the clonal selection theoryThe clonal selectionprinciple is used to describe the main features of an adaptiveimmune response to an antigenic stimulus The main idea isthat only those B cells that identify the antigens are selected toproliferate The selected cells are exposed to an affinity mat-uration process which develops their affinity to the select-ive antigens In this paper no distinction is made between a Bcell and its antibody therefore each individual in our im-mune model will be called B cell
Our previous FAIS and CCS-FAIS classification systemsused population of B cells In these classifiers each B cell had
primary age to live in the population Age of B cells shouldbe increased if their fitness had been improved during thematuration process otherwise those B cells that their currentages reach to their corresponding maximum age thresholdswould die
In this paper we have improved the performance of FAISand CCS-FAIS classifiers The differences of IFAIS (currentpaper method) with CCS-FAIS and FAIS are as follows
(1) In our proposed model we have employed immunememory to remember good B cells during the cloningprocess
(2) We have designed two forms ofmemory to remembergood B cells during the cloning process simple mem-ory and 119896-layer memory
(3) The IFAIS benefits from using several diverse selec-tion procedures to develop an efficient clonal selec-tion algorithm
The goal of the immune model is to obtain a set of ruleswith high accuracy Each B cell represents a rule As we men-tioned in Section 3 each rule is coded according to Figure 1
51 Affinity Functions Equation (4) demonstrates the usedaffinity functions which have been previously presented inCCS-FAIS and FAIS [30 31] Consider
52 Immune Memory The memory cells in natural immunesystem are used for eliminating similar foreign substances Inthis paper we have employed immune memory during thecloning process for selected B cells According to the cloning
Advances in Fuzzy Systems 5
procedure IFAIS
beginInitialization() a population of B cells is generatedRule Generation() a population of B cells searches for optimized rule iterativelyRule Learning() From the final population the best B cell based on fitness is selectedTermination Test If a stopping condition is satisfied the learning of current class is finished andthe algorithm is going to learn the next class
End
Pseudocode 2 Pseudocode of IFAIS
(1) procedure Proposed Classifier(2) do(3) Set current learning class as 119888(4) While Termination Test(5) Generate initial B-cell repertoire from class c antigens(6) While cycle ltMax Iterations (7) Perform Clonal Selection Procedure(8) Use three selection procedures as(9) (1) Roulette Wheel Selection(10) (2) Tournament Selection(11) (3) Uniform Selection(12) Usememory (Simple and k-layered to clone selected B-Cells(13) PerformHyper-mutation(14)
(15) Perform Rule Learning Procedure(16) (1) Select the best B cell(17) (2) Add rule of the best B cell to the current rule set(18) If classification rate is not increased then the current loop exits(19)
(20) Until All classes have been learned
Algorithm 1 An overview of the proposed classifier At initialization a population of B-cells is generated from instances of class 119888 thensome B-cells are selected to proliferate in rule generation phase The life cycle of B-cells is controlled by age The best B-cell is added to ruleset if the classification rate increases more than a threshold At last if the termination test satisfies the classifier learns rules for class 119888
method a B cell is changed randomly Randomness of themodification is a way of exploring in the search space Thebalance of exploration and exploitation is a major problem inheuristic search algorithms In order to exploit the previousknowledge of cloning the memory records the changes of Bcells which enables the algorithm to produce higher quality BcellsThe cloningmethodwith this kind ofmemory increasesthe probability ofmodifications which have been recorded inmemory in former iterations of algorithmWe called this typeof memory simple memory In each iteration the contentsof memory degrade slightly The effectiveness of memorydecreases gradually using the proliferation procedure Whenthe generation of high quality B cells using the memoryis stopped the number of biased memory-based changesdecreases accordingly
During the cloning process it might be more effectiveif we consider more than one modification for the selectedB cell In a simple memory all changes are recorded inde-pendently therefore we define a new type of memory whichis named k-layer memory In this memory type 119896 is themaximum number of simultaneous changes on a B cell For
example a 3-layer memory contains 3 kinds of memoriesThe first memory records just 1 modification the secondmemory records 2 simultaneous modifications and the lastmemory records 3 simultaneous modifications A 119896-layermemory needs a large amount of physical memory to runefficiently therefore it is not a useful method for huge datasetsThedetailed implementation of thesememories has beenexplained in the next section
53 Proposed Classifier An overview of the proposed classi-fier is presented in Pseudocode 2 and Algorithm 1The mainloop of the algorithm applies the learning procedure for eachclass separately This loop consists of 4 steps initializationrule generation rule learning and termination test Rulegeneration phase employs an AIS-based algorithm to finda single rule based on the initiated population In the rulelearning stage when a rule is added to the final learnedrule set the learning mechanism reduces the weight of thosetraining instances that are covered by the new learned ruleTherefore in the next rule generation round the AIS-based
6 Advances in Fuzzy Systems
rule induction procedure focuses on those instances that arecurrently uncovered or misclassified At the beginning of thelearning process the weights of the whole training instancesare set to 1 Each step of the new proposed AIS-based algo-rithm is described briefly in Pseudocode 2 The details ofour algorithm is presented in Algorithm 1 (IFAIS stands forimproved FAIS)
(1) Initialization In this stage a population of B cells isgenerated The number of initial population is constant Thisnumber is a parameter which is named initial Population SizeTo generate a B cell an instance of current class from dataset is selected randomly and fuzzy terms for antecedent partof the rule (B cell) are computed according to each attributevalue of the selected training instance Consequent part of thegenerated rule becomes the class of selected instance Initialage of B cell is another parameter denoted by default AgeAfter generation of initial population fitness is computed foreach B cell independently
(2) Rule Generation In this step a population of B cellssearches for optimized rule iteratively At the first step ofIFAIS some B cells are selected to be cloned This selec-tion is based on roulette-wheel selection algorithm B cellswith higher fitness have more chance to be selected Thenumber of selected B cells is constant (selection Size) Nowit is time to proliferate the selected B cells Hypermutationoccurred during the cloning process A B cell contains arule and the rule has antecedents Hypermutation considersa change to these antecedents which causes a change to thecorresponding B cell Maximum number of simultaneouschanges in antecedents of a B cell would be determined by aparameter which is named max Term Changes Number Weneed to restrict the number of changes because increasingthe number of modified antecedents of a rule increases theprobability of corruption of that rule significantly Now arandom number is generated to determine the number ofchanges to the selected B cell (max value is max TermChanges Number) after that the algorithm determines whichantecedents must be changed using immune memory In thisalgorithm simple memory is presented by a matrix Rowsare fuzzy terms columns are attributes and entry (119894 119895) isthe value of changing jth attribute to 119894th fuzzy term so theprobability of choosing jth attribute is sum of jth columnentries divided by sum of all entries and the probability ofchanging to a fuzzy term is proportional to the value of eachfuzzy termThe determination of correct factor which wouldbe able to reveal the progress of a change is critical In thisalgorithm we use relative affinity (difference of new affinityand old affinity) as value of a change to a fuzzy term If thealgorithm uses 119896-layer memory we should note that 119896 is thesame as max Term Changes Number The 119896-layer memorycontains 119896 matrices Dimension of 1-matrix is like simplememory 119901-matrix is used when 119901 simultaneous changesoccurred therefore the number of columnswould be equal tothe number of attributes or 119862 (attributes 119901) and the numberof rows would be the same as num of fuzzy terms119901 If wedo not use memory the probability of changing an attributevalue to do not care is a parameter that is called dont Care
Replacement Rate The effect of memory controls by weightmeans of default probability and memory probability Thisweight is a parameter which is called memory Weight Num-ber of clones produced for each B cell is another parameterwhich is called clone Number The age of generated B cellsis calculated using (5) This equation controls the populationsize Consider
Agenew = Ageold + Agedefault times affinity
if affinitynew gt affinityold(5)
After cloning B cells of previous generations becameolder Some B cells would be deleted from the main popu-lation because their age reaches 0
(3) Rule Learning When AIS algorithm is finished the fittestB cell is selected The rule which is represented by this B cellis added to the final resulted rule set Then the classificationrate of current rule set is compared to the old rule set whichdoes not contain the new rule Classification rate is calculatedusing (6) If the difference is higher than a threshold (accuracyThreshold) the addition is accepted Consider
classification rate = NCPnumber of patterns
(6)
(4) Termination Test If a stopping condition is satisfied thelearning of current class is finished and the algorithm is goingto learn the next class If the condition is not satisfied thealgorithm tries to learn another rule by initializing a newpopulation for the next execution of AIS We can use anystopping condition for terminating the loop We limit thenumber of learned rules for each class This is done by aparameter which is calledmax Rule Set Size
54 Classification Reasoning Technique After rule extractionprocedure the classifier must employ these learned rulesto predict the class of a test record The usual reasoningmethod of fuzzy classifiers is based on (3) which is explainedin Section 4 in detail We use (3) to predict the class ofan input test instance whenever all of the rules are notapplicable for the input test instance The algorithm finds themost similar rule to this instance In this method a rule iscreated from the instance like the initialization phase primaryrules are generated from instances The most similar rule isthe rule which has the highest length of longest commonsubsequence (LCS) with the newly generated ruleThe lengthof common subsequence of the selected rule must be greaterthanminimum lengthThis value is another parameter whichis named min Rule Similarity Length This method decreasesthe number of unclassified instances of the algorithm
6 Experimental Results
In this section two credit data sets were used to evaluatethe predictive accuracy of the proposed classifier Australiancredit approval and German credit approval data sets areavailable from UCI Machine Learning Repository In Aus-tralian credit approval data set all names and values have
Advances in Fuzzy Systems 7
Table 1 UCI datasets used in our experiments Instances of theAustralian are almost equally distributed between classes but in theGerman they are more unbalanced
Dataset Number ofclasses
Number ofattributes
Number ofinstances Classes
Australian 2 14 690 307 negative383 positive
German 2 24 1000 700 negative300 positive
Table 2 Parameter specification of IFAIS in our experiments
Parameter Value in Australian Value in Germaninitial Population Size 100 300max Iteration 50 50default Age 5 5selection Size 100 100clone Number 10 10max Term Changes Number 3 2dontCare Replacement Rate 05 02max Rule Set Size 5 10accuracy Threshold 003 003max Rule Similarity Length 10 17min Covered Percent 0 30memory Weight 05 05119908119875 001 035119908NCP 069 01119908119873 001 045119908NMP 029 01119908BF 08 0999119908LEN 02 0001
been changed to meaningless to protect confidentiality of thedata Table 1 illustrates the information of these data setsIn Australian credit data there are 383 instances where as-signing credit to them has high risk and 307 instances arecreditworthy applicants The German credit data is more un-balanced and it consists of 300 instances where creditshould not be assigned and 700 instances are creditworthyapplicants
Each value in the Australian and German data setsis normalized between 00 and 10 using the min-maxtransformation method Table 2 represents the parametersettings that have been used in IFAIS Simulations havebeen performed by Weka data mining tool Table 2 shows aninteresting fact about the used datasets the German creditscoring dataset is more complicated than Australian creditscoring dataset This is because of the need of IFAIS to workwith a greater initial population size and maximum rule setsize when it is applied on the German credit scoring dataset
In Figures 2 and 3 the progress of classification rate perrule of the proposed classifier for Australian and Germancredit data sets has been illustrated respectivelyThese figuresillustrate the role of each evolved fuzzy if-then rule for the twoused datasets Our algorithm uses iterative rule learning andit employs AIS per iteration to find a rule (rule generation
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule
Figure 2 Progress of classification rate per rule of IFAIS forAustralian credit data set
100
90
80
70
60
50
40
30
20
10
0
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Figure 3 Progress of classification rate per rule of IFAIS forGermancredit data set
phase) After the extraction of each rule the weights ofinstances that have been covered by the rule are decreased InIFAIS the instances are removed from data set which meansthe weights are set to zero According to Figures 2 and 3 thefirst extracted rules are more general and shorter than laterrules All of the extracted rules participate in the decision-making process and the rules classify almost the whole testdata
According to Figures 2 and 3 we can also compare thecomplexity of data sets To accomplish this we have extracted5 rules for each class of Australian dataset For each class ofthe German dataset we had 12 and 17 rules for negative andpositive classes respectively
The difference in number of extracted rules shows thatGerman data set patterns are more complex than Australian
8 Advances in Fuzzy Systems
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
beginInitialization() a population of B cells is generatedRule Generation() a population of B cells searches for optimized rule iterativelyRule Learning() From the final population the best B cell based on fitness is selectedTermination Test If a stopping condition is satisfied the learning of current class is finished andthe algorithm is going to learn the next class
End
Pseudocode 2 Pseudocode of IFAIS
(1) procedure Proposed Classifier(2) do(3) Set current learning class as 119888(4) While Termination Test(5) Generate initial B-cell repertoire from class c antigens(6) While cycle ltMax Iterations (7) Perform Clonal Selection Procedure(8) Use three selection procedures as(9) (1) Roulette Wheel Selection(10) (2) Tournament Selection(11) (3) Uniform Selection(12) Usememory (Simple and k-layered to clone selected B-Cells(13) PerformHyper-mutation(14)
(15) Perform Rule Learning Procedure(16) (1) Select the best B cell(17) (2) Add rule of the best B cell to the current rule set(18) If classification rate is not increased then the current loop exits(19)
(20) Until All classes have been learned
Algorithm 1 An overview of the proposed classifier At initialization a population of B-cells is generated from instances of class 119888 thensome B-cells are selected to proliferate in rule generation phase The life cycle of B-cells is controlled by age The best B-cell is added to ruleset if the classification rate increases more than a threshold At last if the termination test satisfies the classifier learns rules for class 119888
method a B cell is changed randomly Randomness of themodification is a way of exploring in the search space Thebalance of exploration and exploitation is a major problem inheuristic search algorithms In order to exploit the previousknowledge of cloning the memory records the changes of Bcells which enables the algorithm to produce higher quality BcellsThe cloningmethodwith this kind ofmemory increasesthe probability ofmodifications which have been recorded inmemory in former iterations of algorithmWe called this typeof memory simple memory In each iteration the contentsof memory degrade slightly The effectiveness of memorydecreases gradually using the proliferation procedure Whenthe generation of high quality B cells using the memoryis stopped the number of biased memory-based changesdecreases accordingly
During the cloning process it might be more effectiveif we consider more than one modification for the selectedB cell In a simple memory all changes are recorded inde-pendently therefore we define a new type of memory whichis named k-layer memory In this memory type 119896 is themaximum number of simultaneous changes on a B cell For
example a 3-layer memory contains 3 kinds of memoriesThe first memory records just 1 modification the secondmemory records 2 simultaneous modifications and the lastmemory records 3 simultaneous modifications A 119896-layermemory needs a large amount of physical memory to runefficiently therefore it is not a useful method for huge datasetsThedetailed implementation of thesememories has beenexplained in the next section
53 Proposed Classifier An overview of the proposed classi-fier is presented in Pseudocode 2 and Algorithm 1The mainloop of the algorithm applies the learning procedure for eachclass separately This loop consists of 4 steps initializationrule generation rule learning and termination test Rulegeneration phase employs an AIS-based algorithm to finda single rule based on the initiated population In the rulelearning stage when a rule is added to the final learnedrule set the learning mechanism reduces the weight of thosetraining instances that are covered by the new learned ruleTherefore in the next rule generation round the AIS-based
6 Advances in Fuzzy Systems
rule induction procedure focuses on those instances that arecurrently uncovered or misclassified At the beginning of thelearning process the weights of the whole training instancesare set to 1 Each step of the new proposed AIS-based algo-rithm is described briefly in Pseudocode 2 The details ofour algorithm is presented in Algorithm 1 (IFAIS stands forimproved FAIS)
(1) Initialization In this stage a population of B cells isgenerated The number of initial population is constant Thisnumber is a parameter which is named initial Population SizeTo generate a B cell an instance of current class from dataset is selected randomly and fuzzy terms for antecedent partof the rule (B cell) are computed according to each attributevalue of the selected training instance Consequent part of thegenerated rule becomes the class of selected instance Initialage of B cell is another parameter denoted by default AgeAfter generation of initial population fitness is computed foreach B cell independently
(2) Rule Generation In this step a population of B cellssearches for optimized rule iteratively At the first step ofIFAIS some B cells are selected to be cloned This selec-tion is based on roulette-wheel selection algorithm B cellswith higher fitness have more chance to be selected Thenumber of selected B cells is constant (selection Size) Nowit is time to proliferate the selected B cells Hypermutationoccurred during the cloning process A B cell contains arule and the rule has antecedents Hypermutation considersa change to these antecedents which causes a change to thecorresponding B cell Maximum number of simultaneouschanges in antecedents of a B cell would be determined by aparameter which is named max Term Changes Number Weneed to restrict the number of changes because increasingthe number of modified antecedents of a rule increases theprobability of corruption of that rule significantly Now arandom number is generated to determine the number ofchanges to the selected B cell (max value is max TermChanges Number) after that the algorithm determines whichantecedents must be changed using immune memory In thisalgorithm simple memory is presented by a matrix Rowsare fuzzy terms columns are attributes and entry (119894 119895) isthe value of changing jth attribute to 119894th fuzzy term so theprobability of choosing jth attribute is sum of jth columnentries divided by sum of all entries and the probability ofchanging to a fuzzy term is proportional to the value of eachfuzzy termThe determination of correct factor which wouldbe able to reveal the progress of a change is critical In thisalgorithm we use relative affinity (difference of new affinityand old affinity) as value of a change to a fuzzy term If thealgorithm uses 119896-layer memory we should note that 119896 is thesame as max Term Changes Number The 119896-layer memorycontains 119896 matrices Dimension of 1-matrix is like simplememory 119901-matrix is used when 119901 simultaneous changesoccurred therefore the number of columnswould be equal tothe number of attributes or 119862 (attributes 119901) and the numberof rows would be the same as num of fuzzy terms119901 If wedo not use memory the probability of changing an attributevalue to do not care is a parameter that is called dont Care
Replacement Rate The effect of memory controls by weightmeans of default probability and memory probability Thisweight is a parameter which is called memory Weight Num-ber of clones produced for each B cell is another parameterwhich is called clone Number The age of generated B cellsis calculated using (5) This equation controls the populationsize Consider
Agenew = Ageold + Agedefault times affinity
if affinitynew gt affinityold(5)
After cloning B cells of previous generations becameolder Some B cells would be deleted from the main popu-lation because their age reaches 0
(3) Rule Learning When AIS algorithm is finished the fittestB cell is selected The rule which is represented by this B cellis added to the final resulted rule set Then the classificationrate of current rule set is compared to the old rule set whichdoes not contain the new rule Classification rate is calculatedusing (6) If the difference is higher than a threshold (accuracyThreshold) the addition is accepted Consider
classification rate = NCPnumber of patterns
(6)
(4) Termination Test If a stopping condition is satisfied thelearning of current class is finished and the algorithm is goingto learn the next class If the condition is not satisfied thealgorithm tries to learn another rule by initializing a newpopulation for the next execution of AIS We can use anystopping condition for terminating the loop We limit thenumber of learned rules for each class This is done by aparameter which is calledmax Rule Set Size
54 Classification Reasoning Technique After rule extractionprocedure the classifier must employ these learned rulesto predict the class of a test record The usual reasoningmethod of fuzzy classifiers is based on (3) which is explainedin Section 4 in detail We use (3) to predict the class ofan input test instance whenever all of the rules are notapplicable for the input test instance The algorithm finds themost similar rule to this instance In this method a rule iscreated from the instance like the initialization phase primaryrules are generated from instances The most similar rule isthe rule which has the highest length of longest commonsubsequence (LCS) with the newly generated ruleThe lengthof common subsequence of the selected rule must be greaterthanminimum lengthThis value is another parameter whichis named min Rule Similarity Length This method decreasesthe number of unclassified instances of the algorithm
6 Experimental Results
In this section two credit data sets were used to evaluatethe predictive accuracy of the proposed classifier Australiancredit approval and German credit approval data sets areavailable from UCI Machine Learning Repository In Aus-tralian credit approval data set all names and values have
Advances in Fuzzy Systems 7
Table 1 UCI datasets used in our experiments Instances of theAustralian are almost equally distributed between classes but in theGerman they are more unbalanced
Dataset Number ofclasses
Number ofattributes
Number ofinstances Classes
Australian 2 14 690 307 negative383 positive
German 2 24 1000 700 negative300 positive
Table 2 Parameter specification of IFAIS in our experiments
Parameter Value in Australian Value in Germaninitial Population Size 100 300max Iteration 50 50default Age 5 5selection Size 100 100clone Number 10 10max Term Changes Number 3 2dontCare Replacement Rate 05 02max Rule Set Size 5 10accuracy Threshold 003 003max Rule Similarity Length 10 17min Covered Percent 0 30memory Weight 05 05119908119875 001 035119908NCP 069 01119908119873 001 045119908NMP 029 01119908BF 08 0999119908LEN 02 0001
been changed to meaningless to protect confidentiality of thedata Table 1 illustrates the information of these data setsIn Australian credit data there are 383 instances where as-signing credit to them has high risk and 307 instances arecreditworthy applicants The German credit data is more un-balanced and it consists of 300 instances where creditshould not be assigned and 700 instances are creditworthyapplicants
Each value in the Australian and German data setsis normalized between 00 and 10 using the min-maxtransformation method Table 2 represents the parametersettings that have been used in IFAIS Simulations havebeen performed by Weka data mining tool Table 2 shows aninteresting fact about the used datasets the German creditscoring dataset is more complicated than Australian creditscoring dataset This is because of the need of IFAIS to workwith a greater initial population size and maximum rule setsize when it is applied on the German credit scoring dataset
In Figures 2 and 3 the progress of classification rate perrule of the proposed classifier for Australian and Germancredit data sets has been illustrated respectivelyThese figuresillustrate the role of each evolved fuzzy if-then rule for the twoused datasets Our algorithm uses iterative rule learning andit employs AIS per iteration to find a rule (rule generation
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule
Figure 2 Progress of classification rate per rule of IFAIS forAustralian credit data set
100
90
80
70
60
50
40
30
20
10
0
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Figure 3 Progress of classification rate per rule of IFAIS forGermancredit data set
phase) After the extraction of each rule the weights ofinstances that have been covered by the rule are decreased InIFAIS the instances are removed from data set which meansthe weights are set to zero According to Figures 2 and 3 thefirst extracted rules are more general and shorter than laterrules All of the extracted rules participate in the decision-making process and the rules classify almost the whole testdata
According to Figures 2 and 3 we can also compare thecomplexity of data sets To accomplish this we have extracted5 rules for each class of Australian dataset For each class ofthe German dataset we had 12 and 17 rules for negative andpositive classes respectively
The difference in number of extracted rules shows thatGerman data set patterns are more complex than Australian
8 Advances in Fuzzy Systems
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
rule induction procedure focuses on those instances that arecurrently uncovered or misclassified At the beginning of thelearning process the weights of the whole training instancesare set to 1 Each step of the new proposed AIS-based algo-rithm is described briefly in Pseudocode 2 The details ofour algorithm is presented in Algorithm 1 (IFAIS stands forimproved FAIS)
(1) Initialization In this stage a population of B cells isgenerated The number of initial population is constant Thisnumber is a parameter which is named initial Population SizeTo generate a B cell an instance of current class from dataset is selected randomly and fuzzy terms for antecedent partof the rule (B cell) are computed according to each attributevalue of the selected training instance Consequent part of thegenerated rule becomes the class of selected instance Initialage of B cell is another parameter denoted by default AgeAfter generation of initial population fitness is computed foreach B cell independently
(2) Rule Generation In this step a population of B cellssearches for optimized rule iteratively At the first step ofIFAIS some B cells are selected to be cloned This selec-tion is based on roulette-wheel selection algorithm B cellswith higher fitness have more chance to be selected Thenumber of selected B cells is constant (selection Size) Nowit is time to proliferate the selected B cells Hypermutationoccurred during the cloning process A B cell contains arule and the rule has antecedents Hypermutation considersa change to these antecedents which causes a change to thecorresponding B cell Maximum number of simultaneouschanges in antecedents of a B cell would be determined by aparameter which is named max Term Changes Number Weneed to restrict the number of changes because increasingthe number of modified antecedents of a rule increases theprobability of corruption of that rule significantly Now arandom number is generated to determine the number ofchanges to the selected B cell (max value is max TermChanges Number) after that the algorithm determines whichantecedents must be changed using immune memory In thisalgorithm simple memory is presented by a matrix Rowsare fuzzy terms columns are attributes and entry (119894 119895) isthe value of changing jth attribute to 119894th fuzzy term so theprobability of choosing jth attribute is sum of jth columnentries divided by sum of all entries and the probability ofchanging to a fuzzy term is proportional to the value of eachfuzzy termThe determination of correct factor which wouldbe able to reveal the progress of a change is critical In thisalgorithm we use relative affinity (difference of new affinityand old affinity) as value of a change to a fuzzy term If thealgorithm uses 119896-layer memory we should note that 119896 is thesame as max Term Changes Number The 119896-layer memorycontains 119896 matrices Dimension of 1-matrix is like simplememory 119901-matrix is used when 119901 simultaneous changesoccurred therefore the number of columnswould be equal tothe number of attributes or 119862 (attributes 119901) and the numberof rows would be the same as num of fuzzy terms119901 If wedo not use memory the probability of changing an attributevalue to do not care is a parameter that is called dont Care
Replacement Rate The effect of memory controls by weightmeans of default probability and memory probability Thisweight is a parameter which is called memory Weight Num-ber of clones produced for each B cell is another parameterwhich is called clone Number The age of generated B cellsis calculated using (5) This equation controls the populationsize Consider
Agenew = Ageold + Agedefault times affinity
if affinitynew gt affinityold(5)
After cloning B cells of previous generations becameolder Some B cells would be deleted from the main popu-lation because their age reaches 0
(3) Rule Learning When AIS algorithm is finished the fittestB cell is selected The rule which is represented by this B cellis added to the final resulted rule set Then the classificationrate of current rule set is compared to the old rule set whichdoes not contain the new rule Classification rate is calculatedusing (6) If the difference is higher than a threshold (accuracyThreshold) the addition is accepted Consider
classification rate = NCPnumber of patterns
(6)
(4) Termination Test If a stopping condition is satisfied thelearning of current class is finished and the algorithm is goingto learn the next class If the condition is not satisfied thealgorithm tries to learn another rule by initializing a newpopulation for the next execution of AIS We can use anystopping condition for terminating the loop We limit thenumber of learned rules for each class This is done by aparameter which is calledmax Rule Set Size
54 Classification Reasoning Technique After rule extractionprocedure the classifier must employ these learned rulesto predict the class of a test record The usual reasoningmethod of fuzzy classifiers is based on (3) which is explainedin Section 4 in detail We use (3) to predict the class ofan input test instance whenever all of the rules are notapplicable for the input test instance The algorithm finds themost similar rule to this instance In this method a rule iscreated from the instance like the initialization phase primaryrules are generated from instances The most similar rule isthe rule which has the highest length of longest commonsubsequence (LCS) with the newly generated ruleThe lengthof common subsequence of the selected rule must be greaterthanminimum lengthThis value is another parameter whichis named min Rule Similarity Length This method decreasesthe number of unclassified instances of the algorithm
6 Experimental Results
In this section two credit data sets were used to evaluatethe predictive accuracy of the proposed classifier Australiancredit approval and German credit approval data sets areavailable from UCI Machine Learning Repository In Aus-tralian credit approval data set all names and values have
Advances in Fuzzy Systems 7
Table 1 UCI datasets used in our experiments Instances of theAustralian are almost equally distributed between classes but in theGerman they are more unbalanced
Dataset Number ofclasses
Number ofattributes
Number ofinstances Classes
Australian 2 14 690 307 negative383 positive
German 2 24 1000 700 negative300 positive
Table 2 Parameter specification of IFAIS in our experiments
Parameter Value in Australian Value in Germaninitial Population Size 100 300max Iteration 50 50default Age 5 5selection Size 100 100clone Number 10 10max Term Changes Number 3 2dontCare Replacement Rate 05 02max Rule Set Size 5 10accuracy Threshold 003 003max Rule Similarity Length 10 17min Covered Percent 0 30memory Weight 05 05119908119875 001 035119908NCP 069 01119908119873 001 045119908NMP 029 01119908BF 08 0999119908LEN 02 0001
been changed to meaningless to protect confidentiality of thedata Table 1 illustrates the information of these data setsIn Australian credit data there are 383 instances where as-signing credit to them has high risk and 307 instances arecreditworthy applicants The German credit data is more un-balanced and it consists of 300 instances where creditshould not be assigned and 700 instances are creditworthyapplicants
Each value in the Australian and German data setsis normalized between 00 and 10 using the min-maxtransformation method Table 2 represents the parametersettings that have been used in IFAIS Simulations havebeen performed by Weka data mining tool Table 2 shows aninteresting fact about the used datasets the German creditscoring dataset is more complicated than Australian creditscoring dataset This is because of the need of IFAIS to workwith a greater initial population size and maximum rule setsize when it is applied on the German credit scoring dataset
In Figures 2 and 3 the progress of classification rate perrule of the proposed classifier for Australian and Germancredit data sets has been illustrated respectivelyThese figuresillustrate the role of each evolved fuzzy if-then rule for the twoused datasets Our algorithm uses iterative rule learning andit employs AIS per iteration to find a rule (rule generation
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule
Figure 2 Progress of classification rate per rule of IFAIS forAustralian credit data set
100
90
80
70
60
50
40
30
20
10
0
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Figure 3 Progress of classification rate per rule of IFAIS forGermancredit data set
phase) After the extraction of each rule the weights ofinstances that have been covered by the rule are decreased InIFAIS the instances are removed from data set which meansthe weights are set to zero According to Figures 2 and 3 thefirst extracted rules are more general and shorter than laterrules All of the extracted rules participate in the decision-making process and the rules classify almost the whole testdata
According to Figures 2 and 3 we can also compare thecomplexity of data sets To accomplish this we have extracted5 rules for each class of Australian dataset For each class ofthe German dataset we had 12 and 17 rules for negative andpositive classes respectively
The difference in number of extracted rules shows thatGerman data set patterns are more complex than Australian
8 Advances in Fuzzy Systems
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
Table 1 UCI datasets used in our experiments Instances of theAustralian are almost equally distributed between classes but in theGerman they are more unbalanced
Dataset Number ofclasses
Number ofattributes
Number ofinstances Classes
Australian 2 14 690 307 negative383 positive
German 2 24 1000 700 negative300 positive
Table 2 Parameter specification of IFAIS in our experiments
Parameter Value in Australian Value in Germaninitial Population Size 100 300max Iteration 50 50default Age 5 5selection Size 100 100clone Number 10 10max Term Changes Number 3 2dontCare Replacement Rate 05 02max Rule Set Size 5 10accuracy Threshold 003 003max Rule Similarity Length 10 17min Covered Percent 0 30memory Weight 05 05119908119875 001 035119908NCP 069 01119908119873 001 045119908NMP 029 01119908BF 08 0999119908LEN 02 0001
been changed to meaningless to protect confidentiality of thedata Table 1 illustrates the information of these data setsIn Australian credit data there are 383 instances where as-signing credit to them has high risk and 307 instances arecreditworthy applicants The German credit data is more un-balanced and it consists of 300 instances where creditshould not be assigned and 700 instances are creditworthyapplicants
Each value in the Australian and German data setsis normalized between 00 and 10 using the min-maxtransformation method Table 2 represents the parametersettings that have been used in IFAIS Simulations havebeen performed by Weka data mining tool Table 2 shows aninteresting fact about the used datasets the German creditscoring dataset is more complicated than Australian creditscoring dataset This is because of the need of IFAIS to workwith a greater initial population size and maximum rule setsize when it is applied on the German credit scoring dataset
In Figures 2 and 3 the progress of classification rate perrule of the proposed classifier for Australian and Germancredit data sets has been illustrated respectivelyThese figuresillustrate the role of each evolved fuzzy if-then rule for the twoused datasets Our algorithm uses iterative rule learning andit employs AIS per iteration to find a rule (rule generation
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule
Figure 2 Progress of classification rate per rule of IFAIS forAustralian credit data set
100
90
80
70
60
50
40
30
20
10
0
PositiveNegativeTotal
Clas
sifica
tion
accu
racy
()
Rule1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Figure 3 Progress of classification rate per rule of IFAIS forGermancredit data set
phase) After the extraction of each rule the weights ofinstances that have been covered by the rule are decreased InIFAIS the instances are removed from data set which meansthe weights are set to zero According to Figures 2 and 3 thefirst extracted rules are more general and shorter than laterrules All of the extracted rules participate in the decision-making process and the rules classify almost the whole testdata
According to Figures 2 and 3 we can also compare thecomplexity of data sets To accomplish this we have extracted5 rules for each class of Australian dataset For each class ofthe German dataset we had 12 and 17 rules for negative andpositive classes respectively
The difference in number of extracted rules shows thatGerman data set patterns are more complex than Australian
8 Advances in Fuzzy Systems
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
Table 3 Predictive accuracy of FAIS and different classifiers
Classifier Australian GermanAIRS1 Weka version of [66] 832 6871AIRS2 Weka version of [66] 8441 6964AIRS as conventional AIS [9] 852 713CCS-FAIS [55] 807 711CLONALG Weka version of [59] 8222 6642CSCAlowast 8478 7017DMNBtext 8258 6999DTNB 8541 7152FAIS [30] 8551 72Immunos-1lowast 7612 6138Immunos-99lowast 7672 6367LibSVM 8551 7098LWL 8551 70Kstar 7888 6989PART 8332 7011SAIS [9] 852 754SMO with RBFKernel 8551 70IFAIS using simple memory 8652 723IFAIS using 3-layer memory 8783 749The results have been obtained using Weka machine learning toolThe order of classifiers is alphabetical The most accurate is bold and thesecond most is italicComparison of predictive accuracies illustrated our proposed algorithm iscompetitive with other classifierslowastmeans classifiers which have been manually added to Weka and areavailable at httpwekaclassalgossourceforgenet
data set (In Figure 3 the increasing rate of graph for negativeclass is higher than the same class in Figure 2)
The negative class in German data set has more com-plicated signature because in comparison to Australian dataset the later learned rules have more effects (the steep of thegraph is very slow) This fact shows that achieving accurateknowledge for Australian data set is more difficult thanGerman data set In Australian data set the first rules are veryimportant because final classification accuracy is nearly equalto the classification accuracy at those points
In Table 1 we have demonstrated the distribution of in-stances over the two classes of Australian and German creditscoring datasets In Australian data set this distribution isapproximately equal Figure 3 shows this fact too because theaccuracy of classes are nearly the same In German data setthe number of negative class instances is more than instancesof positive class In Figure 3 we have seen the important roleof negative class in final classification accuracyThe extractedrules of positive class have covered very few test records Wefollowed 10-fold cross-validation procedure to evaluate theaccuracy of our classifier The classification rate is measuredwith Weka machine learning software and compared withwell-known classifiers in Weka including LibSVM PARTDTNB Kstar LWL DMNBtext SMO with RBFKernel andJ48 In these classifiers DTNB and PART extract rules J48uses decision tree LWL andKstar are lazy classifiers LibSVMand SMO are two implementations of SVM and DMNBtext
Table 4 Confusion matrix
Actual PredictedNegative Positive
Negative TN FPPositive FN TP
Table 5 Comparing precision recall and 119865-measure of IFAIS andselected classifiers
SMO with RBFKernelPrecision 093 079 infin 07Recall 08 093 00 10
F-measure 086 085 infin 082The results are measured by Weka machine learning software The order ofclassifiers is alphabeticalThe best result is bold and the secondmost is italic
uses Bayesian decision theory Table 3 summarizes the pre-diction accuracies of the proposed algorithms and otherclassifiers In this table other AIS-based algorithms are alsodemonstrated Other performance measures for comparingour classifier with mentioned classifiers are precision recalland 119865-measure These measures can be obtained using (7)and according to Table 4 Consider
recallNEG =TN
TN + FPrecallPOS = TP
TP + FN
precisionNEG =TN
TN + FNprecisionPOS = TP
TP + FP
119865-measure = 2 times precision times recallprecision + recall
(7)
According to Table 5 our proposed algorithm has themost value in119865-measure in both positive and negative classes
Advances in Fuzzy Systems 9
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
(except in positive class for Australian data set that the valueis the second best) 119865-measure is the harmonic mean of pre-cision and recall The significance of precision and recall isdependent to the domain In some application areas precisionis more interested than recall and in some others recallis more important But with 119865-measure we consider bothprecision and recall measures concurrently Therefore IFAISis a reliable learning algorithm for classification problems
7 Conclusion
In this paper we proposed a fuzzy classification system forcredit scoring named IFAISTheproposed classifier combinesfuzzy logic andAIS conceptsThenewproposed classificationsystem was an enhanced version of FAIS and CCS-FAISclassifiers as the two earlier versions of AIS-based classifi-cation system for credit scoring In our proposed IFAIS weused immune memory to remember good B cells duringthe cloning process We designed two forms of memorysimple memory and 119896-layer memory Results indicated thatour new definition of memory for immune-based fuzzy ruleextraction increases the final classification rate of credit riskprediction significantly
According to the promising results that we have obtainedusing the immune principles is very effective for credit riskprediction therefore we will consider other concepts in arti-ficial immune systems like negative selection or immunenetwork as our future work
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] H A Abdou ldquoGenetic programming for credit scoring thecase of Egyptian public sector banksrdquo Expert Systems withApplications vol 36 no 9 pp 11402ndash11417 2009
[2] L J Mester ldquoWhats the point of credit scoringrdquo BusinessReview vol 3 pp 3ndash16 1997
[3] L Zhang X Hui and LWang ldquoApplication of adaptive supportvector machines method in credit scoringrdquo in Proceedings ofthe 16th International Conference on Management Science andEngineering (ICMSE rsquo09) pp 1410ndash1415 September 2009
[4] S Vukovic B Delibasic A Uzelac and M Suknovic ldquoA case-based reasoningmodel that uses preference theory functions forcredit scoringrdquo Expert Systems with Applications vol 39 no 9pp 8389ndash8395 2012
[5] B W Yap S H Ong and N H M Husain ldquoUsing data miningto improve assessment of credit worthiness via credit scoringmodelsrdquo Expert Systems with Applications vol 38 no 10 pp13274ndash13283 2011
[6] W Gang and M Jian ldquoA hybrid ensemble approach for enter-prise credit risk assessment based on Support Vector MachinerdquoExpert Systems with Applications vol 39 no 5 pp 5325ndash53312012
[7] X Zhou W Jiang Y Shi and Y Tian ldquoCredit risk evaluationwith kernel-based affine subspace nearest points learningmethodrdquo Expert Systems with Applications vol 38 no 4 pp4272ndash4279 2011
[8] D L Olson andD DWu ldquoReview of innovative CSR from riskmanagement to value creationrdquo Journal of Cleaner Production vol 18 no 16 pp 1767ndash1768 2010
[9] K Leung F Cheong and C Cheong ldquoConsumer credit scoringusing an artificial immune system algorithmrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC rsquo07) pp3377ndash3384 Singapore September 2007
[10] E Altman ldquoFinancial ratios discriminant analysis and the pre-diction of corporate bankruptcyrdquo Journal of Finance vol 23 no4 pp 589ndash609 1968
[11] P A Lachenbruch Discriminant Analysis Hafner New YorkNY USA 1975
[12] W E Henley and D J Hand ldquoA k-nearest-neighbour classifierfor assessing consumer credit riskrdquo Journal of the Royal Statis-tical Society Series D The Statistician vol 45 no 1 pp 77ndash951996
[13] Y E Orgler ldquoA credit scoring model for commercial loansrdquoJournal of Money Credit Bank pp 435ndash445 1970
[14] S Finlay ldquoCredit scoring for profitability objectivesrdquo EuropeanJournal of Operational Research vol 202 no 2 pp 528ndash5372010
[15] D Wu and D L Olson ldquoEnterprise risk management copingwith model risk in a large bankrdquo Journal of the OperationalResearch Society vol 61 no 2 pp 179ndash190 2010
[16] D Wu and D L Olson ldquoEnterprise risk management smallbusiness scorecard analysisrdquo Production Planning amp Controlvol 20 no 4 pp 362ndash369 2009
[17] D D Wu and D L Olson ldquoIntroduction to the special sectionon lsquooptimizing risk management Methods and toolsrsquordquo Humanand Ecological Risk Assessment vol 15 no 2 pp 220ndash226 2009
[18] D D Wu X Kefan L Hua Z Shi and D L Olson ldquoModelingtechnological innovation risks of an entrepreneurial team usingsystem dynamics an agent-based perspectiverdquo TechnologicalForecasting and Social Change vol 77 no 6 pp 857ndash869 2010
[19] D D Wu and D Olson ldquoEnterprise risk management a DEAVaR approach in vendor selectionrdquo International Journal ofProduction Research vol 48 no 16 pp 4919ndash4932 2010
[20] D D Wu and D L Olson ldquoIntroduction to special sectionon rdquoRisk and Technologyldquordquo Technological Forecasting and SocialChange vol 77 no 6 pp 837ndash839 2010
[21] L Wang and C Fang ldquoAn effective shuffled frog-leaping algo-rithm for multi-mode resource-constrained project schedulingproblemrdquo Information Sciences vol 181 no 20 pp 4804ndash48222011
[22] Y Wen H Xu and J Yang ldquoA heuristic-based hybrid genetic-variable neighborhood search algorithm for task schedulingin heterogeneous multiprocessor systemrdquo Information Sciencesvol 181 no 3 pp 567ndash581 2011
[23] J Yang H Xu and P Jia ldquoEffective search for Pittsburgh learn-ing classifier systems via estimation of distribution algorithmsrdquoInformation Sciences vol 198 pp 100ndash117 2012
[24] L Yu ldquoAn evolutionary programming based asymmetricweighted least squares support vector machine ensemble learn-ing methodology for software repository miningrdquo InformationSciences vol 191 pp 31ndash46 2012
10 Advances in Fuzzy Systems
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
[25] R Zhang and C Wu ldquoBottleneck machine identificationmethod based on constraint transformation for job shop sched-uling with genetic algorithmrdquo Information Sciences vol 188 pp236ndash252 2012
[26] V S Desai J N Crook and G A Overstreet Jr ldquoA comparisonof neural networks and linear scoringmodels in the credit unionenvironmentrdquo European Journal of Operational Research vol95 no 1 pp 24ndash37 1996
[27] J EHunt andD E Cooke ldquoLearning using an artificial immunesystemrdquo Journal of Network and Computer Applications vol 19no 2 pp 189ndash212 1996
[28] J Timmis and T Knight ldquoArtificial immune systems using theimmune system as inspiration for dataminingrdquo inDataMiningA Heuristic Approach pp 209ndash230 Group Idea Publishing2001
[29] J Timmis A Hone T Stibor and E Clark ldquoTheoretical advan-ces in artificial immune systemsrdquoTheoretical Computer Sciencevol 403 no 1 pp 11ndash32 2008
[30] E Kamalloo and M S Abadeh ldquoAn artificial immune systemfor extracting fuzzy rules in credit scoringrdquo in Proceedings ofthe IEEE Congress on Evolutionary Computation (CEC 10) pp1ndash8 Barcelona Spain July 2010
[31] E Kamalloo andM S Abadeh ldquoComprehensible credit scoringwith fuzzy artificial immune systemrdquo in Proceedings of the 18thIranianConference on Electrical Engineering (ICEE 10) pp 542ndash547 Isfahan Iran May 2010
[32] M Hall E Frank G Holmes B Pfahringer P Reutemann andI H Witten ldquoThe WEKA data mining software an updaterdquoACM SIGKDD Explorations Newsletter vol 11 no 1 pp 10ndash182009
[33] C Huang M Chen and C Wang ldquoCredit scoring with a datamining approach based on support vector machinesrdquo ExpertSystems with Applications vol 33 no 4 pp 847ndash856 2007
[34] P Yao ldquoHybrid classifier using neighborhood rough set andSVM for credit scoringrdquo in Proceedings of the InternationalConference on Business Intelligence and Financial Engineering(BIFE rsquo09) pp 138ndash142 Beijing China July 2009
[35] D Zhang M Hifi Q Chen andW Ye ldquoA hybrid credit scoringmodel based on genetic programming and support vectormachinesrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 8ndash12 October 2008
[36] J Yi ldquoCredit scoring model based on the decision tree andthe simulated annealing algorithmrdquo in Proceedings of the WRIWorld Congress on Computer Science and Information Engineer-ing (CSIE rsquo09) pp 18ndash22 Los Angeles Calif USA April 2009
[37] M F A Gadi X Wang and A P Do Lago ldquoCredit cardfraud detection with artificial immune systemrdquo Lecture Notesin Computer Science vol 5132 pp 119ndash131 2008
[38] W-C Yeh ldquoNovel swarm optimization formining classificationrules on thyroid gland datardquo Information Sciences vol 197 pp65ndash76 2012
[39] Z Pei G Resconi A J van der Wal K Qin and Y XuldquoInterpreting and extracting fuzzy decision rules from fuzzyinformation systems and their inferencerdquo Information Sciencesvol 176 no 13 pp 1869ndash1897 2006
[40] M J Zolghadri and E G Mansoori ldquoWeighting fuzzy clas-sification rules using receiver operating characteristics (ROC)analysisrdquo Information Sciences vol 177 no 11 pp 2296ndash23072007
[41] X Chang and J H Lilly ldquoEvolutionary design of a fuzzy clas-sifier fromdatardquo IEEETransactions on SystemsMan andCyber-netics B vol 34 no 4 pp 1894ndash1906 2004
[42] Z Lei and L Ren-Hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[43] A Frank and A Asuncion UCI Machine Learning Repository2010 httparchiveicsucieduml
[44] D Yang L Jiao M Gong and F Liu ldquoArtificial immune multi-objective SAR image segmentation with fused complementaryfeaturesrdquo Information Sciences vol 181 no 13 pp 2797ndash28122011
[45] J Zhao Q LiuWWang ZWei and P Shi ldquoA parallel immunealgorithm for traveling salesman problem and its application oncold rolling schedulingrdquo Information Sciences vol 181 no 7 pp1212ndash1223 2011
[46] Y Zhong L Zhang B Huang and P Li ldquoAn unsupervised arti-ficial immune classifier for multihyperspectral remote sensingimageryrdquo IEEE Transactions on Geoscience and Remote Sensingvol 44 no 2 pp 420ndash431 2006
[47] L N de Castro and F J von Zuben ldquoLearning and optimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002
[48] D Dasgupta ldquoAdvances in artificial immune systemsrdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 40ndash432006
[49] J Greensmith U Aickelin andG Tedesco ldquoInformation fusionfor anomaly detection with the dendritic cell algorithmrdquo Infor-mation Fusion vol 11 no 1 pp 21ndash34 2010
[50] Z Jinquan L Xiaojie L Tao L Caiming P Lingxi and SFeixian ldquoA self-adaptive negative selection algorithm used foranomaly detectionrdquo Progress in Natural Science vol 19 no 2pp 261ndash266 2009
[51] R R Sumar A A Rodrigues Coelho and L D Santos CoelholdquoUse of an artificial immune network optimization approach totune the parameters of a discrete variable structure controllerrdquoExpert Systems with Applications vol 36 no 3 pp 5009ndash50152009
[52] K Tan C Goh AMamun and E Ei ldquoAn evolutionary artificialimmune system for multi-objective optimizationrdquo EuropeanJournal ofOperational Research vol 187 no 2 pp 371ndash392 2008
[53] H Y K Lau V W K Wong and I S K Lee ldquoImmunity-basedautonomous guided vehicles controlrdquo Applied Soft ComputingJournal vol 7 no 1 pp 41ndash57 2007
[54] G Luh and W Liu ldquoAn immunological approach to mobilerobot reactive navigationrdquo Applied Soft Computing Journal vol8 no 1 pp 30ndash45 2008
[55] E Hart and J Timmis ldquoApplication areas of AIS the past thepresent and the futurerdquo Applied Soft Computing Journal vol 8no 1 pp 191ndash201 2008
[56] W Wang S Gao and Z Tang ldquoA complex artificial immunesystemrdquo in Proceedings of the 4th International Conference onNatural Computation (ICNC rsquo08) pp 597ndash601 Jinan ChinaOctober 2008
[57] K Polat and S Gunes ldquoA hybrid medical decision makingsystem based on principles component analysis k-NN basedweighted pre-processing and adaptive neuro-fuzzy inferencesystemrdquo Digital Signal Processing vol 16 no 6 pp 913ndash9212006
[58] X Shen X Z Gao R Bie and X Jin ldquoArtificial immune net-works models and applicationsrdquo in Proceedings of the Inter-national Conference on Computational Intelligence and Security(ICCIAS rsquo06) pp 394ndash397 October 2006
Advances in Fuzzy Systems 11
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
[59] L de Castro and F von Zuben ldquoaiNet an artificial immune net-work for data analysisrdquo in Data Mining A Heuristic Approachpp 231ndash259 Group Idea Publishing 2001
[60] J Kelsey and J Timmis ldquoImmune inspired somatic contiguoushypermutation for function optimisationrdquo in Genetic and Evo-lutionary Computation (GECCO rsquo03) 2003
[61] H Ishibuchi K Nozaki N Yamamoto and H Tanaka ldquoSelect-ing fuzzy if-then rules for classification problems using geneticalgorithmsrdquo IEEE Transactions on Fuzzy Systems vol 3 no 3pp 260ndash270 1995
[62] O Cordon and F Herrera ldquoA three-stage evolutionary processfor learning descriptive and approximate fuzzy-logic-controllerknowledge bases from examplesrdquo International Journal ofApproximate Reasoning vol 17 no 4 pp 369ndash407 1997
[63] F Hoffmann ldquoCombining boosting and evolutionary algo-rithms for learning of fuzzy classification rulesrdquo Fuzzy Sets andSystems vol 141 no 1 pp 47ndash58 2004
[64] K Nozaki H Ishibuchi and H Tanaka ldquoAdaptive fuzzyrule-based classification systemsrdquo IEEE Transactions on FuzzySystems vol 4 no 3 pp 238ndash250 1996
[65] M S Abadeh J Habibi M Daneshi M Jalali and MKhezrzadeh ldquoIntrusion detection using a hybridization ofevolutionary fuzzy systems and artificial immune systemsrdquo inProceedings of the IEEE Congress on Evolutionary Computation(CEC rsquo07) pp 3547ndash3553 September 2007
[66] A Watkins J Timmis and L Boggess ldquoArtificial immune rec-ognition system (AIRS) An immune-inspired supervisedlearning algorithmrdquo Genetic Programming and Evolvable Ma-chines vol 5 no 3 pp 291ndash317 2004
