A review on the applications of type-2 fuzzy logic in classification and pattern recognition

Expert Systems with Applications xxx (2013) xxx–xxx

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Expert Systems with Applications

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Review

A review on the applications of type-2 fuzzy logic in classificationand pattern recognition

0957-4174/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.eswa.2013.03.020

⇑ Corresponding author. Tel./fax: +52 664 6236318.E-mail addresses: [email protected], [email protected] (P. Melin).

Please cite this article in press as: Melin, P., & Castillo, O. A review on the applications of type-2 fuzzy logic in classification and pattern recognitionSystems with Applications (2013), http://dx.doi.org/10.1016/j.eswa.2013.03.020

Patricia Melin ⇑, Oscar CastilloTijuana Institute of Technology, Clzada Tecnologico s/n, Fracc. Tomas Aquino, 22379 Tijuana, BC, Mexico

a r t i c l e i n f o

Keywords:Type-2 fuzzy logicPattern RecognitionClassificationClustering

a b s t r a c t

In this paper a review of type-2 fuzzy logic applications in pattern recognition, classification and cluster-ing problems is presented. Recently, type-2 fuzzy logic has gained popularity in a wide range of applica-tions due to its ability to handle higher degrees of uncertainty. In particular, there have been recentapplications of type-2 fuzzy logic in the fields of pattern recognition, classification and clustering, whereit has helped improving results over type-1 fuzzy logic. In this paper a concise and representative reviewof the most successful applications of type-2 fuzzy logic in these fields is presented.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Uncertainty affects decision-making and emerges in a numberof different forms. The concept of information is inherently associ-ated with the concept of uncertainty. The most fundamental aspectof this connection is that the uncertainty involved in any problem-solving situation is a result of some information deficiency, whichmay be incomplete, imprecise, fragmentary, not fully reliable, va-gue, contradictory, or deficient in some other way. Uncertainty isan attribute of information. The general framework of fuzzy rea-soning allows handling much of this uncertainty and fuzzy systemsemploy type-1 fuzzy sets, which represent uncertainty by numbersin the range [0,1]. When an entity is uncertain, like a measure-ment, it is difficult to determine its exact value, and of coursetype-1 fuzzy sets make more sense than sets. However, it is notreasonable to use an accurate membership function for somethinguncertain, so in this case what we need is another type of fuzzysets, those which are able to handle these uncertainties, the socalled type-2 fuzzy sets (Karnik and Mendel, 1998). The amountof uncertainty in a system can be reduced by using type-2 fuzzy lo-gic because this logic offers better capabilities to handle linguisticuncertainties by modeling vagueness and unreliability of informa-tion (Castillo & Melin, 2008).

Type-2 fuzzy models have emerged as an interesting general-ization of fuzzy models based upon type-1 fuzzy sets. There havebeen a number of claims put forward as to the relevance of type-2 fuzzy sets being regarded as generic building constructs of fuzzymodels (Melin & Castillo, 2005). Likewise, there is a record of someexperimental evidence showing some improvements in terms ofaccuracy of fuzzy models of type-2 over their type-1 counterparts

(Castillo & Melin, 2008). Unfortunately, no systematic and compre-hensive design framework has been provided and while improve-ments over type-1 fuzzy models were evidenced, it is not clearwhether this effect could always be expected. Furthermore, it isnot demonstrated whether the improvement is substantial enoughand fully legitimized given the substantial optimization overheadassociated with the design of this category of models. There havebeen a lot of applications of type-2 in intelligent control, patternrecognition, intelligent manufacturing, time series prediction, andothers (Castillo & Melin, 2008; Karnik & Mendel, 1998; Melin &Castillo, 2005; Melin, 2010). However, in this paper we will con-centrate on applications in clustering, classification and patternrecognition.

The rest of the paper is structured as follows. Section 2 offers abrief overview of the basic concepts of type-2 fuzzy systems. Sec-tion 3 provides a concise review of type-2 fuzzy logic applicationsin clustering and classification. Section 4 presents a representativereview of type-2 fuzzy logic applications in image processing andpattern recognition. Finally, section 5 presents the conclusions.

2. Type-2 fuzzy systems

In this section, a brief overview of type-2 fuzzy systems is pre-sented. This overview is intended to provide the basic conceptsneeded to understand the methods and algorithms presented laterin the paper (Herman et al., 2008; Juang, Huang, & Lin, 2009).

The structure of the type-2 fuzzy rules is the same as for thetype-1 case because the distinction between type-2 and type-1 isassociated with the nature of the membership functions (Karnik& Mendel, 1998). Hence, the only difference is that now some orall the sets involved in the rules are of type-2. In a type-1 fuzzy sys-tem, where the output sets are type-1 fuzzy sets, we perform

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Fig. 2. Interval type-2 membership function.

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defuzzification in order to get a number, which is in some sense acrisp (type-0) representative of the combined output sets. In thetype-2 case, the output sets are type-2; so we have to use extendedversions of type-1 defuzzification methods (Castillo & Melin, 2008).

If for a type-1 membership function, we blur it to the left and tothe right, as illustrated in Fig. 1, then a type-2 membership func-tion is produced. In this case, for a specific value x0, the member-ship function (u0), takes on different values, which are not allweighted the same, so we can assign membership grades to all ofthose points.

By doing this for all x e X, we form a three-dimensional mem-bership function –a type-2 membership function– that character-izes a type-2 fuzzy set (Juang et al., 2009). A type-2 fuzzy set eA,is characterized by the membership function:

eA ¼ fððx;uÞ;leAðx;uÞÞj8x 2 X; 8u 2 Jx # ½0;1�g ð1Þ

in which 0 6 leAðx; uÞ 6 1. In fact Jx # [0, 1] represents the primary

membership of x, and leAðx;uÞ is a type-1 fuzzy set known as the

secondary set. Hence, a type-2 membership grade can be any subsetin [0,1], the primary membership, and corresponding to each pri-mary membership, there is a secondary membership (which canalso be in [0,1]) that defines the possibilities for the primary mem-bership. Uncertainty is represented by a region, which is called thefootprint of uncertainty (FOU). When leAðx; uÞ ¼ 1; 8 u 2 Jx # ½0;1�we have an interval type-2 membership function, as shown inFig. 2. The uniform shading for the FOU represents the entire inter-val type-2 fuzzy set and it can be described in terms of an uppermembership function �leAðxÞ and a lower membership function

leAðxÞ.An FLS described using at least one type-2 fuzzy set is called a

type-2 FLS. Type-1 FLSs are unable to directly handle rule uncer-tainties, because they use type-1 fuzzy sets that are certain (viz,fully described by single numeric values). On the other hand,type-2 FLSs, are useful in circumstances where it is difficult todetermine an exact numeric membership function, and there aremeasurement uncertainties.

A type-2 FLS is characterized by IF-THEN rules, where theirantecedent or consequent sets are now of type-2. Type-2 FLSs,can be used when the circumstances are too uncertain to deter-mine exact membership grades such as when the training data isaffected by noise. Similarly, to the type-1 FLS, a type-2 FLS includes

Fig. 1. Type-2 membership function as a blurred type-1 membership function.

Please cite this article in press as: Melin, P., & Castillo, O. A review on the applicSystems with Applications (2013), http://dx.doi.org/10.1016/j.eswa.2013.03.020

a fuzzifier, a rule base, fuzzy inference engine, and an output pro-cessor, as we can see in Fig. 3 (in this case, a fuzzy system with twoinputs and one output is used as illustration). The output processorincludes type-reducer and defuzzifier; it generates a type-1 fuzzyset output (from the type-reducer) or a number (from the defuzz-ifier) (Juang et al., 2009). Now we explain each of the blocks shownin Fig. 3.

2.1. Fuzzifier

The fuzzifier maps a numeric vector x = (x1, . . . ,xp)T e X1 �X2�. . .�Xp � X into a type-2 fuzzy set eAx in X (Juang et al., 2009),an interval type-2 fuzzy set in this case. We use type-2 singletonfuzzifier, in a singleton fuzzification, the input fuzzy set has onlya single point on nonzero membership. eAx is a type-2 fuzzy single-ton if leAx

ðxÞ ¼ 1=1 for x = x0 and leAxðxÞ ¼ 1=0 for all other x – x0.

2.2. Rules

The structure of rules in a type-1 FLS and a type-2 FLS is thesame, but in the latter the antecedents and the consequents is rep-resented by type-2 fuzzy sets. So for a type-2 FLS with p inputs x1 -e X1, . . .,xp e Xp and one output y e Y, Multiple Input Single Output(MISO), if we assume there are M rules, the lth rule in the type-2FLS can be written down as follows:

Rl : IF x1 is eF l1 and � � � and xp is eF l

p;

THEN y is eGl l ¼ 1; . . . ;M ð2Þ

2.3. Inference

In the type-2 FLS, the inference engine combines rules and givesa mapping from input type-2 fuzzy sets to output type-2 fuzzy sets.It is necessary to compute the join t, (unions) and the meet P(intersections), as well as the extended sup-star compositions(sup star compositions) of type-2 relations. If eF l

1 � � � � � eF lp ¼ eAl,

(2) can be re-written as follows

Rl : ~Fl1 � � � � � ~Fl

p ! ~Gl ¼ eAl ! ~Gl l ¼ 1; . . . ;M ð3Þ

Rl is described by the membership function lRl ðx; yÞ ¼lRl ðx1; . . . ; xp; yÞ, where

ations of type-2 fuzzy logic in classification and pattern recognition. Expert


Fig. 3. Structure of a type-2 fuzzy logic system.

P. Melin, O. Castillo / Expert Systems with Applications xxx (2013) xxx–xxx 3

lRl ðx; yÞ ¼ leAl!eGlðx; yÞ ð4Þ

can be written as (Karnik & Mendel, 1998):

lRl ðx; yÞ ¼ leAl!eGlðx; yÞ

¼ l~Fl1ðx1Þ u � � � u l~Fl

pðxpÞ u l~Gl ðyÞ½up

i¼1l~FliðxiÞ� u l~Gl ðyÞ ð5Þ

In general, the p-dimensional input to Rl is given by the type-2 fuzzyset eAx whose membership function becomes

leAxðxÞ ¼ l~x1

ðx1Þ u � � � u l~xpðxpÞ ¼ up

i¼1l~xiðxiÞ ð6Þ

where eXiði ¼ 1; . . . ;pÞ are the labels of the fuzzy sets describing theinputs. Each rule Rl determines a type-2 fuzzy set eBl ¼ eAx � Rl suchthat:

l~Bl ðyÞ ¼ leAx�Rl ¼ tx2X leAxðxÞ u lRl ðx; yÞ

h iy 2 Y l ¼ 1; . . . ;M ð7Þ

This dependency is the input/output relation shown in Fig. 3, whichholds between the type-2 fuzzy set that activates a certain rule inthe inference engine and the type-2 fuzzy set at the output of thatengine.

In the FLS, we used interval type-2 fuzzy sets and intersectionunder product t-norm, so the result of the input and antecedentoperations, which are contained in the firing set,Pp

i¼1leF iiðx0i � Flðx0Þ, is an interval type-1 set,

Flðx0Þ ¼�l

f lðx0Þ; f ðx0Þ�

264375 ¼ �l

f l; f

�

264375 ð8Þ

where

f l�ðx0Þ ¼ l�~Fl

1ðx01Þ � � � � � l�~Fl

pðx0pÞ ð9Þ

and

f�lðx0Þ ¼ �l~Fl1ðx01Þ � � � � � �l~Fl

pðx0pÞ ð10Þ

here ⁄ stands for the product operation.

2.4. Type reducer

The type-reducer generates a type-1 fuzzy set output, which isthen converted in a numeric output through running the defuzzifi-er. This type-1 fuzzy set is also an interval set, for the case of our


FLS we used center of sets (cos) type reduction, Ycos, which is ex-pressed as

YcosðxÞ ¼ ½yl; yr � ¼Z

y12½y1l;y1

r �� Z

yM2½yMl;yM

r �

Zf 12½f l

� ;f�1 �

�Z

f M2½f M� ;f�M �

1PM

i¼1f iyiPMi¼1f i

,ð11Þ

This interval set is determined by its two end points, yl and yr,which corresponds to the centroid of the type-2 interval consequentset eGi,

CeGi¼Z

h1 2 Jy1 � � �Z

hN 2 JyN1�PN

i¼1yihiPNi¼1hi

¼ yil; y

ir

� �ð12Þ

before the computation of Ycos (x), we must evaluate equation (12),and its two end points, yl and yr. If the values of fi and yi that areassociated with yl are denoted f i

l and yil , respectively, and the values

of fi and yi that are associated with yr are denoted f ir and yi

r , respec-tively, from Eq. (13), we have

yl ¼PM

i¼1f il yi

lPMi¼1f i

l

ð13Þ

yr ¼PM

i¼1f ir yi

rPMi¼1f i

r

ð14Þ

The values of yl and yr define the output interval of the type-2 fuzzysystem, which can be used to verify if training or testing data arecontained in the output of the fuzzy system.

2.5. Defuzzifier

From the type-reducer, we obtain an interval set Ycos, to defuzz-ify it we use the average of yl and yr, so the defuzzified output of aninterval singleton type-2 FLS is

yðxÞ ¼ yl þ yr

2ð15Þ

Equation (15) produces a final crisp value output to the type-2 fuzzysystem, that although it appears to be simply an average of twotype-1 fuzzy systems, the output of (15) is more complex as de-scribed in Section 2.6.




2.6. Type-2 fuzzy systems cannot be implemented by traditional type-1fuzzy systems

Based on the inference process of Fig. 3, it can be concluded thatthe output of an interval type-2 FLS is the average of two type-1FLSs. However, these two ‘‘type-1 FLSs’’ that are used in the aver-age are fundamentally different from traditional type-1 FLSs, forthe following reasons (Wu, 2011):

(1) Inconsistency: Meaning that the upper and lower member-ship functions of the same interval type-2 FS may be usedsimultaneously in computing each bound of the type-reduced interval.

(2) Adaptiveness: Meaning that the embedded type-1 fuzzy setsused to compute the bounds of the type-reduced intervalchange as input changes.

We can consider both the inconsistency and adaptiveness astwo fundamental differences between interval type-2 FLSs andtype-1 FLSs. This conclusion can be extended to arbitrary intervaltype-2 FLSs as indicated in the following theorems, which proofscan be found in Wu (2011).

Theorem 1. yl in (13) cannot be implemented by a traditional type-1FLS.

Theorem 2. yr in (14) cannot be implemented by a traditional type-1FLS. Based on Theorems 1 and 2, we can easily reach the followingconclusion:

Theorem 3. An IT2 FLS using the Karnik Mendel type-reducer cannotbe implemented by a traditional T1 FLS or a linear combination of sev-eral traditional type-1 FLSs.

Theorem 3 may help understand why interval type-2 FLSs canoutperform type-1 FLSs in modeling a system. There have beenseveral attempts to answer this fundamental question. The earliestargument is that, because of the footprint of uncertainty, an inter-val type-2 FS has more degrees of freedom than a type-1 FS (i.e.,more parameters are needed to describe an IT2 FS than a T1 FS);hence, IT2 FLSs have the potential to outperform T1 FLSs. However,the complete answer is due to the inconsistency and adaptivenesscharacteristics in the calculation of the interval type-2 fuzzyoutputs.

Of course, Theorems 1, 2 and 3 explain why interval type-2 fuz-zy systems can achieve results that are not possible with type-1fuzzy systems, but this is only theoretically speaking. This in facthas been verified in many real world applications in areas suchas, intelligent control, time series prediction, diagnostics and mon-itoring, and more recently in pattern recognition (Melin & Castillo,2005). In these papers, the superiority of type-2 fuzzy logic overtype-1 has been shown with simulation and experimental results,which was expected based on the theoretical results. In fact, thesuperiority of type-2 fuzzy logic is more evident in situations withhigher degrees of uncertainty, noise or non-linearity. In particular,for this paper it is one of the fundamental reasons why it is inter-esting to review the existing applications in clustering, classifica-tion and pattern recognition.

3. Type-2 fuzzy logic in clustering and classification

In this section a representative account of the most successfulapplications of type-2 fuzzy logic in the fields of clustering andclassification is presented. Type-2 fuzzy logic has been incorpo-rated in methods of clustering and classification to allow handlinghigher levels of uncertainty in complex problems. In the applica-


tions presented in this section the superiority of type-2 overtype-1 fuzzy logic has been shown to be significant.

In the proposed approach of Sharma and Bajaj (2009); Sharmaand Bajaj (2010), an interval type-2 fuzzy system for vehicle clas-sification was presented. The class was identified by checking thewheel base, ground clearance and body length of the vehicle,which are taken as axle distance, chassis height and body lengthrespectively. The problem of uncertainty and imperfection in thedata was handled more effectively than type-1 fuzzy or adaptiveneuro-fuzzy inference system. It is clear that the accuracy oftype-2 fuzzy system itself was better than ANFIS and it is appar-ently expected that if the type-2 system is hybridized with neuralnetwork the accuracy will increase significantly.

In Hosseini, Dehmeshki, Barman, Mazinani, and Qanadli (2010),a genetic type-2 fuzzy system for pattern recognition in computeraided detection systems was presented. A computer aided detec-tion (CAD) system suffers from vagueness and imprecision in bothmedical science and image processing techniques. These uncer-tainty issues in the classification components of a CAD system di-rectly influence the accuracy. This work takes advantage of type-2fuzzy sets as three-dimensional fuzzy sets with high potential formanaging uncertainty issues in vague environments. Furthermore,the Genetic algorithm is employed for tuning of the MFs parame-ters and footprint of uncertainty. In order to assess the perfor-mance, the designed IT2FLSs are applied on a lung CADapplication for classification of nodules. The results revealed thatthe Genetic IT2FLS classifier outperforms the equivalent type-1FLS and is capable of capturing more uncertainties.

In the approach of Pimenta and Camargo (2010), the design ofinterval type-2 fuzzy system classifiers using genetic algorithmswas presented. An evolutionary architecture was proposed to gen-erate the rule base and to optimize the membership functions of atype-2 fuzzy classification system. Some experiments have beenrun using different datasets from the UCI Machine Learning Repos-itory in order to validate the proposed approach and to comparethe results with the ones obtained with the Wang and Mendelmethod and a type-1 fuzzy classification system also generatedby the evolutionary architecture proposed here. The results dem-onstrated that the type-2 fuzzy classification system performedbetter than the other classifiers used in the study.

In the proposal of Chumklin, Auephanwiriyakul, andTheera-Umpon (2010), an interval type-2 fuzzy system formicro-calcification detection in mammograms was presented.Mortality rate from this breast cancer is effectively high and rap-idly increasing. The detection at the earlier state can help to reducethe mortality rate. In this work, the application of interval type-2fuzzy system with automatic membership function generationusing the Possibilistic C-Means (PCM) clustering algorithm waspresented. The result was compared with the result from the inter-val type-2 fuzzy logic system with automatic membership functiongeneration using the Fuzzy C-Means (FCM) clustering algorithm.The interval type-2 fuzzy system with PCM membership functionsgeneration produced the best result.

In the approach of Sanz, Fernandez, Bustince, and Herrera(2010), a genetic algorithm for tuning fuzzy ruled based classifica-tion systems was presented. However, the use of this type of mod-els implies a degree of uncertainty in the definition of the fuzzypartitions. In this work the concept of interval-valued fuzzy setwas used to deal with this problem. The aim of this contributionwas to show the improvement in the performance of linguistic fuz-zy rule-based classification systems afterward the application of acooperative tuning methodology between the tuning of the ampli-tude of the support and the lateral tuning applied to the linguisticlabels modeled with interval-valued fuzzy sets.

In the proposal of Wu & Mendel (2010), the classification of bat-tlefield ground vehicles using type-2 fuzzy logic was presented.




The uniqueness of the approach lies in the following. First, to facil-itate prompt decision making, the acoustic features were extractedfrom short time (about 1 s) intervals in which the acoustic mea-surements can be assumed to be stationary. Second, the choicefor the number of rules in the classifier was rationalized by theinformation inherent in the classification problem regarding thenatural models of the vehicles and terrain conditions. And, thirdand finally, interval type-2 fuzzy rules were constructed to takeadvantage of the capabilities of interval type-2 fuzzy sets in mod-eling unknown time-variations and uncertainties.

In Phong and Thien (2009), the classification of cardiac arrhyth-mias using interval type-2 Sugeno model was presented. This pa-per proposes a method to construct type-2 Takagi–Sugeno–Kang(TSK) fuzzy systems for electrocardiogram (ECG) arrhythmic classi-fication. The method using fuzzy C-mean clustering algorithm andthe back-propagation technique to determine parameters of type-2TSK fuzzy classifier was presented. The generalized bell primarymembership function was used to examine the performance ofthe classifier with different shapes of membership functions.

In the proposal of Yu, Xiao, and Zheng (2009), the interval type-2 possibilistic c-means clustering and its applications to fuzzymodeling was presented. This paper described a robust intervaltype-2 possibilistic C-means (IT2PCM) clustering algorithm, whichis actually alternating cluster estimation, but membership func-tions are selected with interval type-2 fuzzy sets by the users.The cluster prototypes are calculated by type reduction combinedwith defuzzification; consequently they could be directly extractedto generate interval type-2 fuzzy rules that can be used to obtain afirst approximation to the interval type-2 fuzzy logic system(IT2FLS). Excellent simulation results were obtained for the prob-lems of classification and forecasting.

In the proposal of Santiago-Sanchez, Reyes-Garcia, andGomez-Gil (2009), type-2 fuzzy sets were applied to the classifica-tion of cries from infants. Crying is an acoustic event that containsinformation about the functioning of the central nervous system,and the analysis of the infant́s crying can be a support in the distin-guishing diagnosis in cases like asphyxia and hyperbilirrubinemia.The classification of baby cry has been considered by the use of dif-ferent types of neural networks and other recognition approaches.In this work a pattern classification algorithm based on type-2 fuz-zy logic for the classification of infant cry was presented.

In the work of Herman et al. (2008), a type-2 fuzzy logic systemfor complex classification problem was presented. The practicalapplicability of brain–computer interface (BCI) technology is lim-ited due to its insufficient reliability and robustness. One of themajor problems in this regard is the extensive variability andinconsistency of brain signal patterns, observed especially in elec-troencephalogram (EEG). This work presented a fuzzy logic (FL) ap-proach to the problem of handling of the resultant uncertaintyeffects. In particular, it outlines the design of a novel type-2 FL sys-tem (T2FLS) classifier within the framework of an EEG-based BCI.

In Chua and Tan (2008), genetic evolved fuzzy classifiers for theproblem of automotive classification are presented. This work wasaimed at investigating if a type-2 fuzzy classifier can deliver a bet-ter performance when there exists an imprecise decision boundarycaused by improper feature extraction method. Genetic Algorithm(GA) was used to tune the fuzzy classifiers under the Pittsburghscheme. The proposed fuzzy classifiers have been successfully ap-plied to an automotive application whereby the classifier needs todetect the presence of human in a vehicle. Results reveal that thetype-2 classifier has the edge over type-1 classifier when the deci-sion boundaries are imprecise and the fuzzy classifier itself has notenough degrees of freedom to construct a suitable boundary.

In the approach of Lucas, Centeno, and Delgado (2008), generaltype-2 fuzzy classifiers for land cover classification are presented.This work proposed a fuzzy classifier based on type-2 fuzzy sets


to be applied in land cover classification. The classifier was builtfrom the available data and considers the merging of informationacquired from different experts. The new method proposed to de-sign the classifier as well as the use of general type-2 fuzzy sets al-lows the modeling of input-output relations and minimize theeffects of uncertainties in the usual fuzzy rule-based classifiers.The experiments carried out attest the efficiency of the proposedgeneral type-2 fuzzy classifier.

In Starczewski, Scherer, Korytkowski, and Nowicki (2008), mod-ular type-2 neuro fuzzy systems were proposed. In this work amodular system which can be converted into a type-2 neuro-fuzzysystem was studied. The rule base of such system consists of trian-gular type-2 fuzzy sets. The modular structure is trained using thebackpropagation method combined with the AdaBoost algorithm.By applying the type-2 neuro-fuzzy system, the modular structureis converted into a compressed form. This allows overcoming thetraining problem of type-2 neuro-fuzzy systems. An illustrativeexample was given to show the efficiency of the proposed ap-proach in the problems of classification.

In Chen, Li, Harrison, and Zhang (2008), type-2 fuzzy logic basedclassifier fusion for support vector machines was presented. To les-sen the sensitivity of different kernels in SVMs classification andimprove SVMs generalization ability, this paper proposes a fuzzyfusion model to combine multiple SVMs classifiers. To better han-dle uncertainties existing in real classification data and in themembership functions (MFs) in the traditional type-1 fuzzy logicsystem (FLS), interval type-2 fuzzy sets were applied to constructa type-2 SVMs fusion FLS. This type-2 fusion architecture takesconsiderations of the classification results from individual SVMsclassifiers and generates the combined classification decision asthe output. The experiments also show that the type-2 fuzzy lo-gic-based SVMs fusion model is better than the type-1 basedSVM fusion model in general.

In Aliev et al. (2011), type-2 fuzzy neural networks with fuzzyclustering and differential evolution optimization are presented.An interesting alternative is to employ type-2 fuzzy sets, whichaugment fuzzy models with expressive power to develop models,which efficiently capture the factor of uncertainty. Type-2 fuzzy lo-gic systems developed with the aid of evolutionary optimizationforms a useful modeling tool subsequently resulting in a collectionof efficient ‘‘If–Then’’ rules. The type-2 fuzzy neural networks takeadvantage of capabilities of fuzzy clustering by generating type-2fuzzy rule base, resulting in a small number of rules and then opti-mizing membership functions of type-2 fuzzy sets present in theantecedent and consequent parts of the rules.

In the proposal of Abiyev, Kaynak, Alshanableh, and Mamedov(2011), a type-2 neuro-fuzzy system based on clustering was ap-plied to system identification and channel equalization. This workdescribed the development of novel type-2 neuro-fuzzy system foridentification of time-varying systems and equalization of time-varying channels using clustering and gradient algorithms. It com-bines the advantages of type-2 fuzzy systems and neural networks.The type-2 fuzzy system allows handling the uncertainties associ-ated with information or data in the knowledge base of the pro-cess. The proposed structure was used for identification andnoise equalization of time-varying systems.

In Zheng, Xiao, Wang, and Wei (2010a), a similarity measure be-tween type-2 fuzzy sets was presented. The fuzzy similarity mea-sure provides the similar degree of two fuzzy sets (FSs) and can beused in various areas. There are numerous studies as to it on type-1fuzzy sets (T1 FSs), but little attention has been received on type-2fuzzy sets (T2 FSs). In this work, a new similarity measure betweeninterval type-2 fuzzy sets (IT2 FSs) was proposed. First, an axiom-atic definition for the new similarity measure was proposed. Then,according to the proposed definition, a computation formula wasestablished. Finally, several examples are presented to explain its




calculation and combine it with Yang and Shih’s clustering methodfor an application of clustering analysis of Gaussian IT2 FSs.

In Abiyev and Kaynak (2010), a type-2 fuzzy neural structure foridentification and control of time varying plants was presented. Insuch situations, the use of fuzzy approaches becomes a viablealternative. However, the systems constructed on the base of type1 fuzzy systems cannot directly handle the uncertainties associ-ated with information or data in the knowledge base of the pro-cess. In this paper, the structure of a type 2 Takagi–Sugeno–Kangfuzzy neural system was presented, and its parameter update rulewas derived based on fuzzy clustering and gradient learning algo-rithm. It is seen that the proposed structure is a potential candidatefor identification and control purposes of uncertain plants, with theuncertainties being handled adequately by type 2 fuzzy sets.

In the proposal of Zheng, Xiao, Wang, and Wei (2010b), a simi-larity measure between general type-2 fuzzy sets and its applica-tion in clustering is proposed. The similarity measure betweenfuzzy sets is an important concept in fuzzy set theory, but littlework as to it has been done on type-2 fuzzy sets. For that, a newsimilarity measure between general type-2 fuzzy sets was pro-posed in this paper. First, an axiomatic definition for the similaritymeasure between general type-2 fuzzy sets was proposed. Then,based on the selected definition, a computation formula by consid-ering the FOU and the secondary membership function was pro-posed. Finally, examples to illuminate its calculation andcombine it with Yang and Shih’s method for an application to clus-tering of type-2 fuzzy data are presented.

In Qin, Kong, Liu, and Xiao (2010), sea surface clustering basedon type-2 fuzzy theory was presented. Spatial data clustering is aneffective method to find interesting spatio–temporal clusteringpatterns. There are many uncertainties in sea surface temperature(SST) clustering, so clustering methods with uncertainty must beused. Type-2 fuzzy theory takes into account the uncertainty ofmembership grade while fuzzy C means (FCM) not. Based on theanalysis of interval type-2 fuzzy C means (IT2FCM), the paper uti-lizes two normal cloud models to express fuzzifiers m1 and m2, anduses two cloud drops to substitute them. The paper applies the im-proved IT2FCM into global SST clustering, and discovers someinteresting climate patterns.

In Albarracin and Melgarejo (20100, an approach for channelequalization based on quasi type-2 fuzzy systems was presented.This work presented a simple approach for the equalization of anonlinear time varying communication channel using a quasitype-2 fuzzy system. Basically, the quasi-type 2 fuzzy equalizer istuned by clustering the output of the channel as it is proposed inprevious reported works for other fuzzy equalizers. The proposedequalizer was compared with type-1 and interval type-2 equaliz-ers. Although, simulation results show that the quasi type-2 fuzzyadaptive filter exhibits better performance for particular levels ofuncertainty, it behaves similarly to the other equalizers in generalterms.

In Ozkan and Turksen (2010), a cluster validity index for type-2fuzziness was proposed. Upper and lower values of the level offuzziness for Fuzzy C-Mean (FCM) clustering methodology havebeen found as 2.6 and 1.4 respectively in previous studies. Thiswork concentrates on the usage of uncertainty associated withthe level of fuzziness in determination of the number of clustersin FCM in any data. A MiniMax e-stable cluster validity index basedon the uncertainty associated with the level of fuzziness within theframework of Interval Valued Type 2 fuzziness was proposed. If thedata have a clustered structure, the optimum number of clustersmay be assumed to have minimum uncertainty under upper andlower levels of fuzziness.

In Pedrycz (2010), human centricity in computing with fuzzysets was presented. The intent of this study was to investigatethe capabilities of granular computing (and computing with fuzzy


sets, in particular) that are available in the currently existingframework to support the design of human-centric systems.Type-2 fuzzy sets can emerge as a result of linguistic interpretationof the original numeric membership grades. The study brings for-ward a detailed algorithmic framework leading to the determina-tion of type-2 fuzzy sets: in the case of aggregation, the principleof justifiable granularity is a computational vehicle while in caseof linguistic interpretation a certain optimization scheme minimiz-ing entropy which associates with the interpretation of member-ship functions through a limited codebook of linguistic labelswas introduced.

In Juang et al. (2009), a recurrent self evolving interval type-2fuzzy neural network for dynamic system processing was pre-sented. This work proposes a recurrent self-evolving intervaltype-2 fuzzy neural network (RSEIT2FNN) for dynamic system pro-cessing. An RSEIT2FNN incorporates type-2 fuzzy sets in a recur-rent neural fuzzy system in order to increase the noise resistanceof a system. The antecedent parts in each recurrent fuzzy rule inthe RSEIT2FNN are interval type-2 fuzzy sets, and the consequentpart is of the Takagi–Sugeno–Kang (TSK) type with intervalweights. The RSEIT2FNN initially contains no rules; all rules arelearned online via structure and parameter learning. TheRSEIT2FNN was applied to simulations of dynamic system identifi-cations and chaotic signal prediction under both noise-free andnoisy conditions.

In a paper by Türks�en (2009), a review of fuzzy systems modelswith an emphasis on fuzzy functions was presented. In this paper,type 1 fuzzy system models known as Zadeh, Takagi–Sugeno andTurks�en models are first reviewed; then potentially future realiza-tions of type 2 fuzzy systems again under the headings of Zadeh,Takagi–Sugeno and Turks�en fuzzy system models, in contrast toType 1 fuzzy system models are presented. Zadeh’s and Takagi–Sugeno’s models are essentially fuzzy rule base (FRB) models,whereas Turks�en’s models are essentially fuzzy function (FF) mod-els. Type 2 fuzzy system models have a higher predictive power. Indata-driven FSM methods discussed here, a fuzzy C-means (FCM)clustering algorithm is used in order to identify the system struc-ture, i.e., either the number of fuzzy rules or alternately the num-ber of FFs.

In Ren, Baron, and Balazinski (2010), high order type-2 Sugenofuzzy models are presented. This work presents the generalizedtype-2 Takagi–Sugeno–Kang (TSK) fuzzy logic system (FLS) inwhich the antecedent or consequent membership functions aretype-2 fuzzy sets and the consequent part a first or higher orderpolynomial function. The architecture of the generalized type-2TSK FLS and its inference engine are based on the Mendel’s first or-der type-2 TSK FLS. The design method of high order system is anextension of the subtractive clustering based type-2 TSK FLS iden-tification algorithm.

In Zhang, Hu, and Liu (2007), rule extraction of interval type-2fuzzy logic systems based on fuzzy c means clustering was pre-sented. An improved clustering algorithm was proposed in thiswork, which originates from Fuzzy c-Means Clustering (FCM).FCM is one of the algorithms used commonly to extract fuzzy rulesfrom type-1 fuzzy logic system. However, its application is merelylimited to dots set. This deficiency is improved in the new algo-rithm, Interval Fuzzy c-Means Clustering (IFCM), which is adequateto deal with interval sets. The enhanced algorithm was based on anew definition of distance between interval data. This work also fo-cuses on extracting fuzzy rules from interval type-2 fuzzy systems.

In Tan, Foo, and Chua (2007), a type-2 fuzzy system for ECGarrhythmic classification was presented. This work was aimed atassessing the feasibility of using a type-2 fuzzy system for ECGarrhythmic beat classification. Three types of ECG signals, namelythe normal sinus rhythm (NSR), ventricular fibrillation (VF) andventricular tachycardia (VT), are considered. Using a combination




of the fuzzy C-means clustering algorithm and the amount of dis-persion in each cluster, a method for designing the antecedenttype-2 MFs of the classifier from a training data set is formulated.

In Qun et al. (2010), type-2 Sugeno fuzzy logic system usingsubtractive clustering was presented. In this work, a subtractiveclustering identification algorithm was introduced to model type-2 Takagi–Sugeno–Kang (TSK) fuzzy logic systems (FLS). The type-2 TSK FLS identification algorithm is an extension of the type-1TSK FLS modeling algorithm. In the type-2 algorithm, subtractiveclustering method is combined with least squares estimation algo-rithms to pre-identify a type-1 FLS form input/output data. Thenusing type-2 TSK FLS theory, expand the type-1 FLS to a type-2TSK FLS. Fuzzy modeling of type-2 TSK FLS was found to be moreeffective than that of type-1 TSK FLS.

In Liang and Mendel (2000a), Liang and Mendel (2000b), theproblem of overcoming time-varying co-channel interferencetype-2 fuzzy adaptive filters was solved. This work presented amethod for overcoming time-varying co-channel interference(CCI) using type-2 fuzzy adaptive filters (FAF). The type-2 FAF isrealized using an un-normalized type-2 Takagi–Sugeno–Kang fuz-zy logic system. A clustering method was used to adaptively designthe parameters of the FAF. Simulation results show that the equal-izers based on type-2 FAFs perform better than the nearest neigh-bor classifiers or the equalizers based on type-1 FAFs when thenumber of co-channels is much large than 1.

In Table 1 a summary of the contributions where type-2 fuzzysystems have been used in clustering and classification is pre-sented. The comparison shown in Table 1 is based on the domainof the problem, if a comparison with type-1 fuzzy logic is provided,and why type-2 fuzzy logic was used by the authors.

4. Type-2 fuzzy logic in pattern recognition

In this section a representative account of the most successfulapplications of type-2 fuzzy logic in the field of pattern recognitionis presented. Type-2 fuzzy logic has been incorporated in methodsof pattern recognition to allow handling higher levels of uncer-tainty in complex problems. In the applications presented in thissection the superiority of type-2 over type-1 fuzzy logic has beenshown to be significant.

In the Hosseini et al. (2010), a genetic type-2 fuzzy logic systemfor pattern recognition in computer aided detection systems waspresented. A computer aided detection (CAD) system suffers fromvagueness and imprecision in both medical science and image pro-cessing techniques. In this paper, an automatic optimized approachfor generating and tuning type-2 Gaussian membership function(MF) parameters and their footprint of uncertainty is proposed.In this approach, two interval type-2 fuzzy logic system (IT2FLS)methods based on the Mamdani rules model are presented fortackling the uncertainty issues in classification problems in patternrecognition. Furthermore, the genetic algorithm is employed fortuning of the MFs parameters and footprint of uncertainty. In orderto assess the performance, the designed IT2FLSs are applied on alung CAD application for classification of nodules. The results re-veal that the Genetic IT2FLS classifier outperforms the equivalenttype-1 FLS and is capable of capturing more uncertainties.

In Melin (20100, interval type-2 fuzzy logic applications in im-age processing and pattern recognition are presented. Intervaltype-2 fuzzy logic can be applied to perform image processingand pattern recognition. In this work a new type-2 fuzzy logicmethod was applied for edge detection in images and the resultswere compared with three different traditional techniques forthe same goal with the type-2 edge detection outperforming theother techniques.


In Lopez, Melin, and Castillo (2010), a comparative study of fea-ture extraction methods of type-1 and type-2 fuzzy logic for pat-tern recognition was presented. In this work a new approach forfeatures extraction methods with type-1 and type-2 fuzzy logicfor pattern recognition systems based on the pixels mean. In thiswork, pattern recognition with fuzzy logic for feature extractionfor ensemble neural networks for the case of fingerprints and usinga fuzzy logic method for response integration was presented. Anensemble neural network of three modules was used. Each moduleis a local expert on person recognition based on their biometricmeasure.

In the approach of Li and Zhang (2010), a hybrid learning algo-rithm based on additional momentum and self adaptive learningrate was proposed. An interval type-2 fuzzy neural network system(IT2FNN) was proposed to handle nonlinear and uncertain systems.The proposed IT2FNN is a combination of the interval type-2 fuzzylogic control (IT2FLC) and the neural network which inherits thebenefits of these two methods. Applied in the pattern recognitionof highway landscape, the simulation results show that the IT2FNNachieves the best tracking performance in comparison with classicbackpropagation algorithm and structural equation modelingmethod.

In the work of Own (2009), a switching between type-2 fuzzysets and intuitionistic fuzzy sets with application to medical diag-nosis was proposed. In this study, the advantage of type-2 fuzzysets is employed, and the switching relation between type-2 fuzzysets and intuitionistic fuzzy sets is defined axiomatically. Theswitching results are applied to show the usefulness of the pro-posed method in pattern recognition and medical diagnosisreasoning.

In Mendoza, Melin, and Castillo (2009), interval type-2 fuzzylogic and modular neural networks for face recognition waspresented. In this work a method for response integration in mul-ti-net neural systems using interval type-2 fuzzy logic and fuzzyintegrals, with the purpose of improving the performance in thesolution of problems with a great volume of information waspresented. In the application two interval type-2 fuzzy inferencesystems (IT2-FIS) were used; the first IT2-FIS was used for featureextraction in the face training data, and the second one to estimatethe relevance of the modules in the multi-net system.

In Kim, Ahn, and Oh (2009), the design of optimized type-2 fuz-zy neural networks and its application was presented. In order todevelop reliable on-site partial discharge (PD) pattern recognitionalgorithm, Type-2 Fuzzy Neural Networks (T2FNNs) optimized bymeans of Particle Swarm Optimization (PSO) were introduced.T2FNNs exploit type-2 fuzzy sets which have a characteristic ofrobustness in the diverse area of intelligence systems. The resultsobtained by the proposed algorithm were compared with that ofconventional Neural Networks (NNs) as well as the existing RadialBasis Function Neural Networks.

In Hidalgo, Castillo, and Melin (2009), type-2 fuzzy inferencesystems as integration methods in modular neural networks formultimodal biometry were proposed. In this work a comparativestudy between fuzzy inference systems as methods of integrationin modular neural networks for multimodal biometry was pre-sented. First, the use of type-1 fuzzy logic and later the approachwith type-2 fuzzy logic were considered. The fuzzy systems weredeveloped using genetic algorithms to handle fuzzy inference sys-tems with different membership functions. The comparative studyof the type-1 and type-2 fuzzy inference systems was made to ob-serve the behavior of the two different integration methods formodular neural networks for multimodal biometry.

In the work of Lopez and Melin (2008a), Lopez and Melin(2008b), response integration in ensemble neural networks withtype-2 fuzzy logic was proposed. This work describes a new ap-proach for response integration in ensemble neural networks using



Table 1Type-2 fuzzy systems in clustering and classification.

Author (s) (pub. Year) Ref. no. Domain of the problem Comparison with type-1

Why type-2 is required for theproblem?

(Sharma & Bajaj, 2009, 2010) (Sharma & Bajaj, 2009, 2010) Vehicle classification Yes Uncertainty and imperfection of data(Hosseini et al., 2010) (Hosseini et al., 2010) Computer aided detection Yes Imprecision in image processing(Pimenta & Camargo, 2010) (Pimenta & Camargo, 2010) classification Yes Imprecision in classification(Chumklin et al., 2010) (Chumklin et al., 2010) Cancer detection Yes Uncertainty in medical classification(Sanz et al., 2010) (Sanz et al., 2010) classification No Imprecision in classification(Wu & Mendel, 2010) (Wu & Mendel, 2010) Vehicle classification Yes Uncertainty in information(Phong & Thien, 2009) (Phong & Thien, 2009) Arrhythmia classification No Uncertainty in medical classification(Yu et al., 2009) (Yu et al., 2009) Classification and

forecastingNo Uncertainty in data

(Santiago-Sanchez et al., 2009) (Santiago-Sanchez et al., 2009) Classification of infant cries No Uncertainty in medical classification(Herman et al., 2008) (Herman et al., 2008) Brain signal classification No Uncertainty in medical classification(Chua & Tan, 2008) (Chua & Tan, 2008) Automotive classification Yes Uncertainty in classification(Lucas et al., 2008) (Lucas et al., 2008) Land cover classification No Uncertainty in classification(Starczewski et al., 2008) (Starczewski et al., 2008) classification No Uncertainty in classification(Chen et al., 2008) (Chen et al., 2008) Classification Yes Uncertainty in classification(Aliev et al., 2011) (Aliev et al., 2011) clustering Yes Uncertainty in clusteringAbiyev et al., 2011 Abiyev et al., 2011 clustering No Uncertainty in clustering(Zheng et al., 2010a) (Zheng et al., 2010a) classification No Uncertainty in classification(Abiyev & Kaynak, 2010) (Abiyev & Kaynak, 2010) clustering No Uncertainty in clustering(Zheng et al., 2010) (Zheng et al., 2010) clustering No Uncertainty in clustering(Qin et al., 2010) (Qin et al., 2010) Climate pattern clustering No Uncertainty in clustering(Albarracin & Melgarejo, 2010) (F. Albarracin & Melgarejo,

2010),Signal clustering Yes Uncertainty in clustering

(Ozkan & Turksen, 2010) (Ozkan & Turksen, 2010) Clustering No Uncertainty in clustering(Pedrycz, 2010) (Pedrycz, 2010) Clustering Yes Uncertainty in granulationJuang et al., 2009 Juang et al., 2009 Clustering Yes Uncertainty in clustering(Türksen, 2009) (Türks�en, 2009) Clustering Yes Uncertainty in clustering(Ren et al., 2010) (Ren et al., 2010) Clustering No Uncertainty in clustering(Zhang et al., 2007) (Zhang et al., 2007) Clustering No Uncertainty in clustering(Tan et al., 2007) (Tan et al., 2007) Classification No Uncertainty in classification(Qun et al., 2010) (Qun et al., 2010) Clustering Yes Uncertainty in clustering(Liang & Mendel, 2000a,

2000b)(Liang & Mendel, 2000a, 2000b) Classification Yes Uncertainty in classification


interval type-2 fuzzy logic. When using ensemble neural networksit is important to choose a good method of response integration toobtain a better identification in pattern recognition. In this work acomparative analysis between interval type-2 fuzzy logic, type-1fuzzy logic and the Sugeno Integral, as response integration meth-ods, in ensemble neural networks was presented. Based on simula-tion results interval type-2 fuzzy logic is shown to be a superiormethod for response integration.

In Lopez, Melin, and Castillo (2008), optimization of responseintegration with fuzzy logic in ensemble neural networks using ge-netic algorithms was presented. In this work a new method for re-sponse integration in ensemble neural networks with type-1 andtype-2 fuzzy logic using genetic algorithms for optimization waspresented. In this work pattern recognition with ensemble neuralnetworks for the case of fingerprints was considered. An ensembleneural network of three modules was used. The response integra-tion method has the goal of combining the responses of the mod-ules to improve the recognition rate of the individual modules. Inthis work the results of a type-2 approach for response integrationthat improves performance over the type-1 logic approaches werepresented.

In Rhee and Choi (2007), interval type-2 membership functiondesign and its application to radial basis function neural networkswas presented. In this work, an interval type-2 fuzzy membershipdesign method and its application to radial basis function (RBF)neural networks was proposed. Type-1 fuzzy memberships whichare computed from the centroid of the interval type-2 fuzzy mem-berships are incorporated into the RBF neural network. The pro-posed membership assignment was shown to improve theclassification performance of the RBF neural network since theuncertainty of pattern data are desirably controlled by intervaltype-2 fuzzy memberships.


In Herman, Prasad, and McGinnity (2007), a support vector en-hanced design of type-2 fuzzy logic approach to motor imagery re-lated to EEG pattern recognition is presented. The significance ofthe initialization procedure in the development of Type-2 fuzzy lo-gic (T2FL) system-based classifiers should be highlighted consider-ing their intrinsically non-linear nature. Initial structureidentification has been recognized as a crucial stage in the designof an interval T2FL (IT2FL) classifier utilized in the framework ofelectroencephalogram (EEG)-based brain–computer interface(BCI). In conjunction with an efficient gradient-based learningalgorithm it has allowed for robust exploitation of T2FL’s capabili-ties to effectively handle uncertainties inherently associated withchanging dynamics of electrical brain activity.

In the approach of Zeng and Liu (2004), type-2 fuzzy hiddenMarkov models for phoneme recognition are proposed. This workpresents a novel extension of Hidden Markov Models (HMMs):type-2 fuzzy HMMs (type-2 FHMMs). The advantage of this exten-sion is that it can handle both randomness and fuzziness withinthe framework of type-2 fuzzy sets (FSs) and fuzzy logic systems(FLSs). Membership functions (MFs) of type-2 fuzzy sets arethree-dimensional. It is the third dimension that provides the addi-tional degrees of freedom that make it possible to handle bothuncertainties. Experimental results show that the type-2 FHMMhas a comparable performance as that of the HMM but is more ro-bust to noise.

In the work of Ozkan and Türks�en (2004), entropy assessmentfor type-2 fuzziness was presented. One of the sources of uncer-tainty, which perhaps is identified as parameter uncertainty, isthe level of fuzziness in fuzzy system modeling. Given the opti-mum number of clusters and the cluster centers, one can exploretype-2 membership values that capture the uncertainty of mem-berships. In this work, variations of type-2 membership values



Table 2Type-2 fuzzy systems in pattern recognition.

Author (s) (pub. Year) Ref. no. Domain of the problem Comparison with type-1 Why type-2 is required for the problem?

(Hosseini et al., 2010) (Hosseini et al., 2010) Computer aided detection Yes Uncertainty in pattern recognition(Melin, 2010) (Melin, 2010) Edge detection Yes Uncertainty in edge detection(Lopez et al., 2010) (Lopez et al., 2010) Fingerprint recognition Yes Uncertainty in fingerprint recognition(Li & Zhang, 2010) (Li & Zhang, 2010) Pattern recognition No Uncertainty in pattern recognition(Own, 2009) (Own, 2009) Medical diagnosis No Uncertainty in diagnosis(Mendoza et al., 2009) (Mendoza et al., 2009) Face recognition Yes Uncertainty in face recognition(Kim et al., 2009) (Kim et al., 2009) Pattern recognition No Uncertainty in pattern recognition(Hidalgo et al., 2009) (Hidalgo et al., 2009) Multimodal recognition Yes Uncertainty in multimodal pattern recognition(Lopez & Melin, 2008) (Lopez & Melin, 2008) Pattern recognition Yes Uncertainty in pattern recognition(Lopez et al., 2008) (Lopez et al., 2008) Fingerprint recognition Yes Uncertainty in fingerprint recognition(Rhee & Choi, 2007) (Rhee & Choi, 2007) Pattern recognition Yes Uncertainty in pattern recognition(Herman et al., 2007) (Herman et al., 2007) EEC pattern recognition No Uncertainty in EEG pattern recognition(Zeng & Liu, 2004) (Zeng & Liu, 2004) Phoneme recognition No Uncertainty in pattern recognition(Ozkan & Türksen, 2004) (Ozkan & Türks�en, 2004) Pattern recognition Yes Uncertainty in pattern recognition(Wang et al., 2004) (Wang et al., 2004) Pattern recognition Yes Uncertainty in pattern recognition(Mitchell, 2005) (Mitchell, 2005) Pattern recognition No Uncertainty in pattern recognition(Madasu et al., 2008) (Madasu et al., 2008) Edge detection Yes Uncertainty in edge detection(Tizhoosh, 2005) (Tizhoosh, 2005) Image thresholding No Uncertainty in Image thresholding


with the entropy measure for an artificially created 12 data setswere explored. Crisp to fuzzy data sets are constructed so that eachdata set has a different standard deviation within each cluster. Re-sults are assessed by means of a particular entropy measure.

In Wang, Cheng, and Lee (2004), dynamical optimal training forinterval type-2 fuzzy neural networks was presented. Type-2 fuzzylogic system (FLS) cascaded with neural network, type-2 fuzzyneural network (T2FNN), is presented in this work to handle uncer-tainty with dynamical optimal learning. A T2FNN consists of atype-2 fuzzy linguistic process as the antecedent part, and thetwo-layer interval neural network as the consequent part. A gen-eral T2FNN is computational-intensive due to the complexity oftype 2 to 1 reduction. Excellent results were obtained for the truckbacking-up control and the identification of nonlinear system,which yield more improved performance than those using type-1FNN.

In the approach of Mitchell (2005), pattern recognition usingtype-2 fuzzy sets was proposed. Type-2 fuzzy sets are a generaliza-tion of the ordinary fuzzy sets in which the membership value foreach member of the set is itself a fuzzy set in [0,1]. A similaritymeasure for measuring the similarity, or compatibility, betweentwo type-2 fuzzy sets was introduced. With this new similaritymeasure it is shown that type-2 fuzzy sets provide us with a natu-ral language for formulating classification problems in patternrecognition.

In Madasu, Hanmandlu, and Vasikarla (2008), a novel approachfor fuzzy edge detection using type-2 fuzzy sets was presented. Anovel approach is presented for edge detection using the area fea-ture at a pixel, since the area characterizes the structure of theedge present in the neighborhood of a pixel. The results of the pro-posed edge detector were compared with other well known edgedetector like Canny, Gradient diffusion operator etc. The edge de-tected image from the proposed approach seems to fare well overothers.

In the approach of Tizhoosh (2005), image thresholding usingtype-2 fuzzy sets was presented. In recent years, various research-ers have introduced new thresholding techniques based on fuzzyset theory to overcome this problem. Regarding images as fuzzysets (or subsets), different fuzzy thresholding techniques havebeen developed to remove the grayness ambiguity/vagueness dur-ing the task of threshold selection. In this work, a new thresholdingtechnique was introduced which processes and uses thresholds astype 2 fuzzy sets.

In Table 2 a summary of the contributions where type-2 fuzzysystems have been used in pattern recognition is presented. The


comparison shown in Table 2 is based on the domain of the prob-lem, if a comparison with type-1 fuzzy logic is provided, and whytype-2 fuzzy logic was used by the authors.

5. General overview of the area and future trend

In this section a general overview of the area of type-2 fuzzysystem in clustering, classification and pattern recognition is pre-sented. Also, possible future trends that we can envision basedon the review of this area are presented. It has been well-knownfor a long time that designing fuzzy systems is a difficult task,and this is especially true in the case of type-2 fuzzy systems. How-ever, problems with a high level of uncertainty and/or noise arebetter handle by type-2 fuzzy systems, which is certainly the casein complex problems of clustering, classification and pattern recog-nition. The use of type-2 fuzzy systems in designing pattern recog-nition systems has become a more common practice in recentyears, which has been accounted for with the review of papers pre-sented in the previous sections. Also, in the case of designing type-2 fuzzy systems the problem is more complicated due to the highernumber of parameters to consider, making it of upmost importancethe use of bio-inspired optimization techniques for achieving theoptimal designs of this sort of systems. We have to mention thatthe search for the papers considered in this review has been doneby using the search engine available in Scopus online system ofElsevier, in which the papers can be searched for by subject or byauthor names. In this sense, an exhaustive search for papers ontype-2 fuzzy systems for pattern recognition was done by usingthe following keywords: type-2 fuzzy pattern recognition, type-2fuzzy system clustering, and type-2 fuzzy system classification. Itis worth mentioning here that the Scopus database of Elsevier con-tains almost all the respected and relevant publications around theworld, so the review that was formed based on the papers found bythe search engine of Scopus can be considered representative ofthe publications in this area.

In general, based on the literature review that was performedwe envision that the number of papers using type-2 fuzzy logicin the areas of clustering, classification and pattern recognition willcontinue to grow in the future years and the main reason is thatreal world problems are becoming more complex and managinghigher volumes of information. Type-2 fuzzy logic offers a moreappropriate modeling approach to handle higher degrees of uncer-tainty in information and for this reason is better suited to managethese problems and people are realizing this fact, the popularity oftype-2 fuzzy logic in these areas will increase.




6. Conclusions

In this paper a representative and concise review of type-2 fuz-zy logic applications in pattern recognition, classification and clus-tering problems was presented. Recently, type-2 fuzzy logic hasgained popularity in a wide range of applications due to its abilityto handle higher degrees of uncertainty. In this paper a concise andrepresentative review of the most successful applications of type-2fuzzy logic in pattern recognition, classification and clusteringproblems was offered. We expect that in the future the numberof applications of type-2 fuzzy logic in these areas will increasedue to the complexity and higher degree of uncertainty of prob-lems in pattern recognition, classification and clustering.

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A review on the applications of type-2 fuzzy logic in classification and pattern recognition

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