A multi-expert system for ranking patents: An approach based on fuzzy pay-off distributions and a...

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Expert Systems with Applications xxx (2013) xxx–xxx

ESWA 8430 No. of Pages 11, Model 5G

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Contents lists available at SciVerse ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

A multi-expert system for ranking patents: An approach based on fuzzypay-off distributions and a TOPSIS–AHP framework

Mikael Collan a,⇑, Mario Fedrizzi b, Pasi Luukka a

a School of Business, Lappeenranta University of Technology, Skinnarilankatu 34, FI-53851 Lappeenranta, Finlandb Department of Industrial Engineering, University of Trento, Via Inama 5, I-38122 Trento, Italy

21222324252627

a r t i c l e i n f o

Keywords:PatentsPay-off methodConsensusPossibilistic momentsTOPSISAHP

28293031

0957-4174/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.eswa.2013.02.012

⇑ Corresponding author. Tel.: +358 505567185.E-mail addresses: [email protected] (M. Collan)

Fedrizzi), [email protected] (P. Luukka).

Please cite this article in press as: Collan, M., eTOPSIS–AHP framework. Expert Systems with Ap

a b s t r a c t

The aim of this paper is to introduce a decision support system that ranks patents based on multipleexpert evaluations. The presented approach starts with the creation of three value scenarios for each con-sidered patent by each expert. These are used for the construction of individual fuzzy pay-off distributionfunctions for the patent value; a consensual fuzzy pay-off distribution is then determined starting fromthe individual distributions. Possibilistic moments are calculated from the consensus pay-off distributionfor each patent and used in ranking them with TOPSIS. It is further showed how the analytic hierarchyprocess (AHP) can be used to include additional decision variables into the patent selection, thus allowingfor a two-tier decision making process. The system is illustrated with a numerical example and theusability of the system and the combination of methods it includes for patent portfolio selection in thereal world context is discussed.

� 2013 Elsevier Ltd. All rights reserved.

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1. Introduction meant only for market valuation of patents that is to say, for the 59
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Ranking and selection of patents is an important issue from thepoint of view of intellectual property (IPR) managers everywhere.It is most often a recurring task in companies that commonly havetheir IPR managers visit the patent and R&D portfolios once ortwice per year, analyzing the composition of the portfolios andmaking decisions about the modification of portfolio composition.New patents may also be considered on continuing basis, empha-sizing the need for tools even further.

One way to quantitatively rank and to select patents is to useestimation of their future value from the point of view of the firmowning them as a measure of goodness. Value to the firm may verywell be the single most important characteristic of a patent. Otherissues that are important in analyzing and ranking patents aremost often non-financial and have to do with strategic criteria,such as fit of the patents to the corporate portfolio and to the fu-ture plans of the firm. Generally, we can say that a good rankingis able to consider both of these types of information, financialand non-financial.

Commonly there are three main approaches for the valuation ofpatents, these are the ‘‘cost approach’’, the ‘‘market method’’, andthe ‘‘income approach’’ also known as the discounted cash-flowmethod (DCF) (e.g., see Reilly & Schweihs, 1998; Smith & Parr,2000). Of these, the cost approach and the market method are

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ll rights reserved.

, [email protected] (M.

t al. A multi-expert system forplications (2013), http://dx.doi.

derivation of an estimate for a sale price for a patent. The DCFmethod is based on the well known principles of present value(PV) and the same principles can be used also in the ‘‘in-house’’valuation of patents, that is, to derive the ‘‘value to the firm’’ ofpatents.

It is important to note that patent analysis is a forward-lookingexercise, as patents are an enabling class of assets that is most of-ten used to secure the future of the firms’ business. This means thatmethods used in the valuation and analysis of patents should beable to take into consideration the (sometimes considerable) esti-mation inaccuracy present in forward-looking estimation, as theestimation of future cash-flows for patents, since it is not realisticto expect anyone to be able to produce precise estimates for future(patent) cash-flows (Karsak, 2006). Using cash-flow scenarios is awidespread practice of modeling the inaccurate and uncertainfuture cash-flows, and it can also be applied to patent analysis(Collan, Fuller, Mezei, & Wang, 2011). Information to support thecreation of cash-flow scenarios can come from systems specificallydesigned for supporting patent analysis, such as are presented (forexample in Camus & Brancaleon, 2003; Huang, Liang, Lin, Tseng, &Chiang, 2011; Littman-Hillmer & Kuckartz, 2009; Park, Kim, Choi, &Yoon, in press), or it can come directly from experts, most oftenfrom within the firm itself. Fuzzy logic is an established way toexpress imprecision precisely and as such is a usable tool alsowhen patent cash-flows are considered. Fuzzy pay-off method,introduced in Collan, Fullér, and Mezei (2009a, 2009b) and furtherpresented in Collan (2012) is a tool for investment analysis and isbased on using cash-flow scenarios to create an asset’s pay-off dis-

ranking patents: An approach based on fuzzy pay-off distributions and aorg/10.1016/j.eswa.2013.02.012

http://dx.doi.org/10.1016/j.eswa.2013.02.012

mailto:[email protected]




http://www.sciencedirect.com/science/journal/09574174

http://www.elsevier.com/locate/eswa


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tribution that is considered as a fuzzy number. The fuzzy pay-offmethod can be employed in the valuation of patents (Collan &Heikkilä, 2011).

As already observed above, patent analysis is a forward-lookingprocedure and there may be differing views about the directionthat the future will take. This observation can be interpreted inthe way that it makes sense to include more than one expert opin-ion when patent analysis is done. This is true for both, for cash-flow information, as well as, for non-cash-flow information.

As budgets for patent portfolios are tight, the firm can afford tokeep only the best patents. This calls for the ranking of the patentsas a basis of selection. It is a fair assumption that the value to thefirm is a key driver in the selection of patents and can be used as afirst basis for patent selection into portfolios. Important other (sec-ondary) considerations may include different non-financial strate-gic selection criteria. This means that one plausible approach to goabout with patent selection is to first rank the patents that arecompeting for a place in the firm’s portfolio based on their valueto the firm, second do a pre-selection of a sub group of the best pat-ents, and third do a complementary analysis to narrow down thenumber of patents to fit the budget, based on the non-financialstrategic criteria.

In this paper, an approach that enables both the financial andnon-financial merits to be included in ranking of patents is pro-posed, while taking into consideration the estimation imprecision,and the differing estimates of multiple experts. This combination isa new contribution that allows a more holistic analysis on patentsto be performed. The way in which the methods used are combinedis new and new to the field of application. Furthermore, we usepossibilistic moments in characterizing fuzzy financial informationand rank patents according to the moments, to the best of ourknowledge the first proposed approach of its kind.

The remainder of the paper is organized as follows. In Section 2the general framework of the system for performing ranking andselection of patents is presented. In Section 3 we continue by pre-senting the construction of pay-off distributions from cash-flowscenarios by each expert for each patent takes place. In Section 4the consensus modeling mechanism to be used to build consensuspay-off distributions from each expert’s pay-off distributions isintroduced. Section 5 starts with the definition of possibilistic mo-ments of fuzzy pay-off distributions and continues with thedescription of the main steps of TOPSIS, used then for producinga preliminary ranking of patents. In Section 6, after a short presen-tation of AHP we show how it can be used to include strategic cri-teria in ranking the patents. In Section 7 the two-tier process isillustrated with a numerical example that includes the selectionof four patents out of twenty candidate patents. Finally, the paperis closed with a discussion and some conclusions.

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2. A blueprint for a multi-expert consensus reaching system forsupporting patent selection

The focus here is to present a system for supporting investmentdecision-making with regards to patents that is, the selection ofpatents. The circumstances under which the system is usable aresuch that there are a number of possible patents that are compet-ing for funding (inclusion in a portfolio) under a budget constraint.The system is based on using three scenarios of managerial cash-flow estimates for each patent, these cash-flow scenarios are usedin the creation of a pay-off distribution for each patent, by eachexpert.

The pay-off distributions for the patents by different experts arelikely to be different from each other, and in order to get an overallsingle pay-off distribution for each patent a consensus among theexperts’ pay-off distributions must be reached. For this a consensus

Please cite this article in press as: Collan, M., et al. A multi-expert system forTOPSIS–AHP framework. Expert Systems with Applications (2013), http://dx.doi.

facilitating method is used and a single consensus pay-off distribu-tion for each patent is created.

From the consensus pay-off distribution for each patent, threepossibilistic moments are calculated: the possibilistic mean, thepossibilistic standard deviation, and the possibilistic skewness.The calculated possibilistic moments are then used in a TOPSISranking of the patents. This ranking is based on the cash-flowinformation for each patent and thus depends on the perceived va-lue for each patent.

The TOPSIS ranking can be used as a basis of a first selection ofpatents. Here it is however proposed that more information is in-cluded into the selection by continuing the analysis with AHP forthe selected number of best patents as ranked by TOPSIS. TheAHP analysis is carried out by a team of ‘‘elected’’ decision-makers,based on ‘‘strategic’’ criteria that take into consideration different,non financial, aspects of the patents.

The approach is illustrated graphically in Fig. 1. The method canalso be described as the following process:

(i) Each expert creates three cash-flow scenarios for eachinvestment alternative: ‘‘maximum possible’’, ‘‘minimumpossible’’, and ‘‘best estimate’’ scenarios.

(ii) From each experts’ scenarios an individual fuzzy value dis-tribution function (pay-off distribution) is created.

(iii) Consensus pay-off distribution is determined from the mul-tiple experts’ pay-off distributions.

(iv) Values of three possibilistic moments are calculated for eachpatent from the consensus pay-off distributions. These arethe possibilistic mean, the possibilistic standard deviation,and the possibilistic skewness of the pay-off distribution.

(v) The calculated possibilistic moments are used in a ranking ofthe patents with TOPSIS.

(vi) ‘‘Elected’’ decision-makers perform an AHP process, basedon relevant strategic criteria, to create the final ranking ofthe patents.

The resulting ranking of the patents can be used in supportingthe patent portfolio selection, a problem that has been considered,for example in Hassanzadeh, Collan, and Modarres (2012). Thesteps of the approach, with background information, are explainedin more detail in the following sections.

3. Creation of cash-flow scenarios and construction of fuzzypay-off distributions

Using scenarios is a widespread practice of modeling the uncer-tain future of projects and assets under imprecise information. Theidea with scenarios is that different future scenarios are thoughtout according to different possible future ‘states of the world’and cash flows or value connected to these states, are estimated.Creating scenarios for patent alternatives can be done based onthe available information about the future (markets, technology,and other issues); the information need not be precise, becausethe scenarios allow for even a very wide variation of the states ofthe world/value. The information used in creating the scenarioscan come from qualitative information gathered and even fromexisting patent/IPR analysis/management systems (Jain, Murty, &Flynn, 1999; Littman-Hillmer & Kuckartz, 2009). Scenarios can beused to complement all three of the above mentioned patent valu-ation method categories.

When the DCF method is used the scenarios normally includethe estimation of (yearly) cost and revenue cash-flows for the dif-ferent scenarios. The yearly cash-flows are estimated by managersby integrating the collected information into cash-flow estimates;this may include estimating the value of benefits that do not nec-



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Fig. 1. The process from data collection to a ready ranking of patents.

Fig. 2. A triangular pay-off distribution.

M. CollanQ1 et al. / Expert Systems with Applications xxx (2013) xxx–xxx 3


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essarily accrue in terms of money. As an example, in van Triest andVis (2007) three types of relevant cash-flows for cost reducing pat-ents are identified, (i) cash-flows due to competitive advantage, (ii)licensing income, and (iii) maintenance costs of the patent.

For stable patents the evaluation of costs may even be ratherstraightforward, especially for the period after the patent has beengranted, but the estimation of revenues is much more difficult. Thisput in other words means that the cost cash-flows are usuallymuch less apart from each other than the revenue cash-flow sce-narios. This means that as cost and revenue cash-flows are aggre-gated for stable patents the revenue cash-flows are the main driverof the scenarios. For patents that are estimated to face litigation thecosts may be more significant (Agliardi & Agliardi, 2011).

For the purposes of our procedure, three scenarios: a maximumpossible, a best estimate, and a minimum possible scenario are cre-ated for each patent, using one of the above methods. It is alsocommonly understood that any outcome ‘between’ these scenariosis possible. The scenario approach is also compatible with and usedin the valuation of other assets (Collan, 2010; Mathews & Datar,2007).

From the present values for the three scenarios of the alterna-tives, that is the maximum possible, the best guess, and the mini-mum possible present value (the NPV of the cash-flows, when theDCF method is used) a so called pay-off distribution can be con-structed. The pay-off distribution is a possibility distribution forthe patent value that is substantially the same as a fuzzy NPV.The pay-off distribution allows one to treat the information withthe pay-off method (Collan, 2012) and connected tools for analysis(Collan et al., 2009a, 2009b). The pay-off distribution is createdfrom cash-flow scenarios with a simple three step process by:

(i) observing that the best guess scenario NPV is the most likelyone and assigning it full degree membership in the set ofexpected outcomes;

(ii) deciding that the maximum possible and the minimum pos-sible scenarios’ NPVs are the upper and lower bounds of thedistribution–there is also a simplifying assumption, ofbounding the distribution: to not consider values higherthan the optimistic scenario and lower than the pessimisticscenario;

(iii) assuming that the shape of the pay-off distribution istriangular.


Fig. 2 shows a graphical illustration of a triangular pay-off dis-tribution. The result is a triangular distribution of outcomes, withthe peak above the best-guess value of the patent with full mem-bership in the set of possible outcomes and the minimum andmaximum possible values bounding the distribution, with a levelof membership in the set of possible outcomes that approacheszero. As a matter of fact, conditions on the triangular pay-off distri-bution that allow us to treat it as a triangular fuzzy number havebeen set.

Definition 1. The membership function of a triangular fuzzynumber is defined as:

lðxÞ ¼1� a�x

a if a� a 6 x 6 a

1� x�ab if a 6 x 6 aþ b

0 otherwise

8><>:
and denoted as (a,a,b). In the context of this paper ‘‘a’’ correspondsto the best guess estimate, ‘‘a � a’’ to the minimum possible esti-mate, and ‘‘a + b’’ to the maximum possible estimate.
The construction of a (triangular) pay-off distribution and thedecision to treat it as a fuzzy number allows one to perform math-ematical operations on it. For the purposes of investment analysisit is suggested that three or four value scenarios are used, becausethey lead to triangular or trapezoidal pay-off distributions (fuzzynumbers). Use of pay-off distributions in the context of investmentvaluation is reported previously for example in Collan (2011),Collan and Heikkilä (2011), Collan and Kinnunen (2011).



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4. Reaching consensus over the agents’ fuzzy pay-offdistribution functions

Denoting with A = {a1, . . . ,an} the set of the fuzzy pay-off distri-bution functions (alternatives), whose estimation depends on theideas, knowledge, attitudes, and motivations of the agents andtherefore are nothing else than individual judgments, the problemwe address now is to introduce a mechanism driving the agents to-wards a consensus about such a judgments. It is assumed that theconsensus process is defined as a dynamic and iterative group dis-cussion process, coordinated by a moderator. The first step of theprocess consists in the representation of preferences of expertswith respect to the set of alternatives. To wit, each expert ex-presses her/his opinion with respect to the fuzzy pay-off distribu-tion function estimated by any other agent. Assuming that theexperts are more familiar with linguistically-based evaluationsthan with numerical ones, we introduce a linguistic term setL = {l1, . . . , lm} whose elements are linguistic labels used to evaluateindividual preferences.

Accordingly, the preferences of the experts are defined as sub-sets of A � A and represented with square matrices whose ele-ments are chosen in L. Calling P(i) the matrix representing thepreference of expert i, its element phk

(i) is a linguistic term denotingthe degree of preference of ah with respect to ak as expressed by ex-pert i. Adopting one of the most widely used approaches to linguis-tically-based decision making, as introduced by Lotfi Zadeh in theframework of fuzzy set theory (Zadeh, 1975, 1983), it is assumedthat the elements of L are semantically represented by triangularfuzzy numbers. Starting from the results obtained in Fedrizzi, Fed-rizzi, and marques Pereira (1999, 2007) and Fedrizzi, Fedrizzi, Pere-ira, and Brunelli (2008a, 2008b) a dynamical process for finding theconsensual fuzzy pay-off distribution is developed, for any givenpatent, on the basis of a cost function C defined as a convex linearcombination of a soft measure of collective dissensus C1, and of aninertial component of opinion changing aversion C2. For a review ofconsensus modeling in the framework of fuzzy preferences seeBrunelli, Fedrizzi, Fedrizzi, and Marques Pereira (2010) and Cabrer-izo, Moreno, Perez, and Herrera-Viedma (2010). Given the matricesP(1), . . . ,P(n) of linguistically-expressed preferences of the experts, inorder to measure their pair wise difference one needs to calculatethe distances between the triangular fuzzy numbers representingtheir elements. In the literature several definitions of distance be-tween fuzzy numbers have been introduced (see e.g., Grzegorzew-ski, 1998; Kaufman & Gupta, 1991; Tran & Duckstein, 2002;Voxman, 1997), and here a distance belonging to a family of dis-tances introduced in Grzegorzewski (1998) is adopted.

Given the two triangular fuzzy numbers x = (dL,x,dR) andy = (eL,y,eR) where x and y are the central values and dL, eL and dR,dR are the left and right spreads respectively.

For each a 2 [0, 1) consider the a-cuts

½xLðaÞ; xRðaÞ� ¼ ½x� dL þ dLa:xþ dR � dRa�; ½yLðaÞ; yRðaÞ�¼ ½y� eL þ eLa:xþ eR � eRa�; ð1Þ

and the following integrals

IL ¼Z 1

0ðxLðaÞ � yLðaÞÞ

2da; IR ¼Z 1

0ðxRðaÞ � yRðaÞÞ

2da: ð2Þ

The distance is

Dðx; yÞ ¼ ðIL þ IRÞ=2 ð3Þ

and is obtained from the family of distances defined in Grzegorzew-ski (1998) putting p = 2, q = 1/2 and skipping the square root. Let usremark that D is not exactly a distance because it does not alwayssatisfy the triangular inequality, nevertheless henceforth, for thesake of simplicity, the term distance is used when referring to D.


Solving the integrals IL and IR we obtain

Dðx; yÞ ¼ d2 þ D2L=6þ D2

R=6þ dðDR � DLÞ=2 ð4Þ

where d = x � y, DL = dL � eL, and DR = dR � eR.Assuming now, for the sake of simplicity, that only two

alternatives are involved, we indicate with p(i) = (dL(i),p(i),dR

(i)) andp(j) = (eL

(i),p(j),eR(j)) the preferences expressed by the agents i and j

respectively. Following the dynamical consensus process intro-duced for first in Fedrizzi et al. (1999) we determine the global dis-sensus measure of the group of experts

C1 ¼14

Xn

i¼1

C1ðiÞ ð5Þ

where the numerical factor 14 has been introduced to simplify the

computations and does not affect in no way the consensus mecha-nism. C1(i) is defined as

C1ðiÞ ¼Xn

jð–iÞ¼1

C1ði; jÞ !

=ðn� 1Þ ð6Þ

and

C1ði; jÞ ¼ f ðDðpðiÞ;pðjÞÞÞ: ð7Þ

f (�) is a scaling function defined as f ðtÞ ¼ � 1b lnð1þ ebðx�aÞÞ, where

a 2 (0, 1) is a threshold parameter and b 2 (0,1) is a free parametercontrolling the polarization of the sigmoid function f0(x) = 1/(1 + eb(x�a)).

The cost for changing the initial preference p(i) of agent i intothe actual preference p(i) is defined as

C2ðiÞ ¼ f ðDðpðiÞ;pðjÞÞÞ ð8Þ

Accordingly, the global opinion changing aversion of the group ofexperts is given by

C2 ¼12

Xn

i¼1

C2ðiÞ ð9Þ

where to 12 the same applies as above for 1

4. The global cost function Cis defined as

C ¼ ð1� kÞC1 þ kC2 ð10Þ

where k 2 [0, 1] is an exogenous parameter representing the rela-tive importance of the inertial component C2 with respect to thedissensus component C1.

The consensual dynamics is based on the minimization of thecost function CðpðiÞÞ ¼ CðdðiÞL ; p

ðiÞ; dðiÞR Þ through the gradient method.The new preference, for any expert, is obtained from the previousone according to the following iterative process

p! p� ¼ p� crC: ð11Þ

The components of the gradientrC are obtained deriving C with re-spect to dðiÞL ;p

ðiÞ, and dðiÞR .

5. TOPSIS-based ranking of the patents depending onpossibilistic moments of the consensual pay-off distributions

N is used to denote a fuzzy number that is, a fuzzy set of realline R with a normal, fuzzy convex and continuous membershipfunction of bounded support (Collan et al., 2009a, 2009b). N(x) isrepresenting the membership function and N1(x) and N2(x) indicaterespectively the left and right membership functions. Aa-cut of N isdefined as

½N�a ¼ fx 2 R : NðxÞP ag;a 2 ½0;1� ð12Þ

and it is a compact subset of R that can be represented as[N]a = [N1(a),N2(a)].



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Here the notion of crisp possibilistic mean of N introduced inCarlsson and Fullér (2001) and Fuller and Majlender (2003) is usedand defined as the arithmetic mean of its lower and upper possibi-listic mean values L(N) and U(N) where

LðNÞ ¼ 2Z 1

0aN1ðaÞda UðNÞ ¼ 2

Z 1

0aN2ðaÞda ð13Þ

Accordingly, L(N) can be interpreted as the lower possibility-weighted average of the minima of the a-cuts and U(N) can be inter-preted as the upper possibility-weighted average of the maxima ofthe a-cuts.

The crisp possibilistic mean value of N is defined as

MeanðNÞ ¼ ðLðNÞ þ UðNÞÞ=2: ð14Þ

Given the triangular fuzzy number x = (dL,x,dR) and its a-cut[x � dL + dLa �x + dR � dRa] we calculate

LðxÞ ¼ x� dL=3 and UðxÞ ¼ xþ dR=3 ð15Þ

and therefore

MeanðxÞ ¼ xþ ðdR � dLÞ=6: ð16Þ

The possibilistic mean in this context gives a central measure, an‘‘expected value’’ of sorts for the value of the patent. The higherthe possibilistic mean the better.

The variance in (12) has been defined through a-cuts as

VarðNÞ ¼ 12

Z 1

0aðN2ðaÞ � N1ðaÞÞ2da: ð17Þ

For the triangle fuzzy number x = (dL ,x,dR) we obtain

VarðxÞ ¼ ðdL þ dRÞ2=24: ð18Þ

Possibilistic variance is a measure of dispersion (width) of the fuzzynumber and in this context tells us how inaccurate the experts’ esti-mates about the patent cash-flows are. Variance is a risk-measure inthe classical financial theory, the less variance there is the better.Based on the skewness of a fuzzy variable as introduced, amongothers, in Hwang and Yoon (1981), we obtain for the triangular fuz-zy number x

SkewnessðxÞ ¼ ðdL þ dRÞ2ðdR � dLÞ=32: ð19Þ

Possibilistic skewness in this context can be interpreted as a mea-sure of potential. The more the triangular fuzzy number (the valueof the patent) is skewed towards the right (high values) the better.Skewness has, in other words, a relationship with the real optionvalue, a measure of potential also used in the analysis of patentsand Rand D projects (see e.g., Carlsson, Fuller, Heikkilä, and Maj-lender, 2007; Hassanzadeh et al., 2012; Mathews & Salmon, 2007).

Then, we proceed to the ranking of the patents with the TOPSISmethod assuming as attributes the three possibilistic moments.TOPSIS (Technique for Order Preference by Similarity to an IdealSolution) method is a popular approach to multiple attribute deci-sion making problems. It was first developed by Hwang and Yoon(Fedrizzi et al., 2008a, 2008b). TOPSIS simultaneously considers thedistances to the positive and negative ideal solution regarding eachalternative and selects the most relative closeness to the ideal solu-tion and the farthest one from the negative ideal solution. The pro-cedure of TOPSIS starts from the construction of an evaluationmatrix X = [xij] where xij denotes score of the ith alternative withrespect to the jth criterion, and can be summarized as follows:

Step 1: Calculation of normalized decision matrix Z = [zij]

536

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PleaseTOPSIS

zij ¼xijffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPm

j¼1x2ij

q ; j ¼ 1; . . . ;m; i ¼ 1; . . . ;n ð20Þ

cite this article in press as: Collan, M., et al. A multi-expert system for–AHP framework. Expert Systems with Applications (2013), http://dx.doi.

Step 2: Calculation of the weighted normalized decision matrixV = [vij]

rankinorg/10.

v ij ¼ zijð�Þwj; j ¼ 1; . . . ;m; i ¼ 1; . . . ;n ð21Þ

Step 3: Determination of the positive and negative ideal solutionA+ and A�:

Aþ ¼ vþ1 ; . . . ;vþn� �

¼ fðmaxjv ijji 2 BÞ; ðminjv ijji 2 CÞg;A� ¼ v�1 ; . . . ;v�n

� �¼ fðminjv ijji 2 BÞ; ðmaxjv ijji 2 CÞg;

ð22Þ

where B is for benefit criteria and C is for cost criteria.Step 4: Calculation of the distance of each alternative from the

positive ideal solution and negative ideal solution:

dþi ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXm

j¼1

v ij � vþj� �2

vuut ; j ¼ 1; . . . ;m

d�i ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXm

j¼1

v ij � v�j� �2

vuut ; j ¼ 1; . . . ;m:

ð23Þ

Step 5: Calculation of the relative closeness to the ideal solutions:

CCi ¼d�i

dþi þ d�i; j ¼ 1; . . . ;m:

Step 6: Ranking of alternatives: The closer the CCi is to one impliesthe higher priority of the ith alternative.

The TOPSIS approach has been used here, starting from possibi-listic moments derived from financial data and using them in rank-ing of the patent alternatives with regards to the financialcharacteristics of each patent.

6. AHP-based strategic ranking of patents

The AHP (Analytic Hierarchy Process) model (Saaty, 1977, 1980,1986, 1987) is a multi-criteria decision making method that em-ploys a procedure of multiple comparisons to rank order alterna-tive solutions to a multi-criteria decision problem. Basically, itprovides us with a set of tools first to evaluate the mutual impor-tance of given criteria, usually located at the different levels of ahierarchical tree-based structure, then to compare the alternativeson each criterion located at the bottom level of the hierarchy, andfinally to synthesize the results onto one total ranking ofalternatives.

The basic assumption in AHP is that one or more decision mak-ers carry out pair-wise comparisons between criteria (or alterna-tives) on a ratio scale such that, for instance, the expression ‘‘ah

is twice better than ak’’ means that the score of ah is two timeshigher than the score of ak. Even a qualitative expression like ‘‘ah

is much better than ak’’ is interpreted in the AHP to mean thatthe score of ah is a times the score of ak, where a is chosen in a suit-able numerical scale.

The set of scores of the numerical scale introduced by Saaty(1980) is {1,2,3,4,5,6,7,8,9}, and the scores have been verbally de-scribed as follows:

1, equal importance3, moderate importance of one over another5, essential or strong importance of one over another7, demonstrated importance of one over another9, extreme importance of one over another2, 4, 6, and 8 intermediate values between adjacent scores,when compromise is needed.

The numerical pair-wise comparisons are recorded in a squarematrix A = [ahk], assuming that the reciprocity condition ahk = 1/

g patents: An approach based on fuzzy pay-off distributions and a1016/j.eswa.2013.02.012


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13 March 2013

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akh is satisfied for h, k = 1, . . . ,n, where n is the number of criteria/alternatives to be pair-wisely compared.

One more condition should be required to guarantee that thepair-wise comparisons are consistent. Let assume, for example,that ah is two times more preferred than ak and ak is three timesmore preferred than al, consistency means that ahshould be pre-ferred six times more than al. It is presumable that due to inabilityof human beings to be precisely knowledgeable in carrying outpair-wise comparisons the matrix A is more or less far from consis-tency Saaty (1980) provided some measures for evaluating the de-gree of inconsistency.

Assuming, for instance, that given the set {a1, . . . ,am} of alterna-tives we wanted to provide a ranking in order to achieve a prede-termine goal, the pair-wise comparisons are carried out withrespect to the given goal and the outcomes are recorded in a matrixA. Calling w1, . . . ,wm(wi > 0, w + � � � + wm = 1) the weights represent-ing the ranking scores of alternatives, in AHP it is assumed thatahk = wh/wk and accordingly the weights are determined using theeigenvalue method, starting from the following equation

Aw ¼ mw; where w ¼ ½w1 . . . wm�T : ð24Þ

When applying AHP, the decision problem is decomposed into ahierarchy, where criteria and sub-criteria at different levels are con-sidered, and alternatives are located at the bottom of the hierarchy.Once the hierarchy is built, the decision makers systematically eval-uate its various elements (criteria, sub-criteria, and alternatives) bycomparing them pair-wisely at each level of the hierarchy as manytimes as the number of elements of the immediately higher level.For each one of the pair-wise comparisons matrix, at each level ofthe hierarchy, the corresponding vector of weights is determinedand the matrix whose columns are the vector of weights is con-structed at any level. The vector of total ranking of alternatives isobtained by multiplying such matrices backwards.

In our approach, six ‘‘strategic’’ criteria that describe differentrelevant aspects of the patents under analysis are used that areincorporated in the second tier of the patent analysis. They are:

1. Strategic fit of patent/patent family to the portfolio (balance ofthe portfolio)

2. Technical quality of the patent as seen by the expert3. Licensing (Out/Cross) potential of the patent4. Ability to ‘‘disturb competitors’ activities’’5. Ability to open new markets/ preparation for the future6. Ability to protect company’s own activity (against others’ IPR)

The ranking of the patents is carried out by starting from thehierarchical structure represented in Fig. 3.

The procedure is settled as follows: from each of these criteriawe construct a comparison matrix, also known as reciprocalmatrix A. In practice, (in this case) each decision maker made sixreciprocal matrices. These are all aggregated over the decision

R

Strategic fit Technical quality Licensingpoten�a

R

Strategicfit Technicalquality Licensingpoten�a

GOAL

CRITERIA

ALTERNATIVES Patent 1 Patent 2

Fig. 3. Hierarchical structure for


makers to get consensus reciprocal matrices. This is done by usinggeometric mean, as often is used in the literature (Xu, 2000).

aij ¼Ymk¼1

ðaijkÞbk ; i; j ¼ 1; . . . ;n; k ¼ 1; . . . ;m ð25Þ

Here we simply use bk ¼ 1m for the importance of the k’th decision

and this way decide not to discriminate between the decision mak-ers. From the reciprocal matrices we then compute the largesteigenvalues and corresponding eigenvectors. Procedure is shortlyas follows:

(1) Sum up each column of the matrix and divide each elementof the matrix by its column sum to get the normalized rela-

tive weight: fWij¼

aijPn

i¼1aij

(2) Sum fW ij up for each row to get: fW i ¼Pn

j¼1fW ij

(3) Normalize Wi: Wi ¼eW iPn

i¼1eW i

(4) Calculate the approximation of the largest eigenvaluekmax ¼ 1

n

Pni¼1ðAWÞi

Wi

Matlab’s built-in functions are used to calculate eigenvaluesand eigenvectors. After this the normalized principal eigenvector,also known as the priority vector of A, is computed for all criteria.

Consistency tests are run for each criterion, by computing theconsistency index (CI) and the consistency ratio (CR).

CI ¼ kmax � nn� 1

CR ¼ CIRI

ð26Þ

where RI is a random consistency index.The consistency ratio is used to determine, whether the possible

inconsistency is at an acceptable level and the standard thresholdcriteria CR < 0.1 is used. Next, the overall composite for each alter-native is computed. This is a normalization of the linear combina-tions of the chosen priority vectors. This composition vector is thenused to form the final ranking of patents.

7. Numerical example

This numerical example uses the discounted cash-flow method(DCF) approach to patent valuation, and looks at how a set of pat-ents, competing for entry into a patent portfolio can be ranked.Starting point is a situation where one already is in the possessionof NPV information for three cash-flow scenarios for twenty pat-ents that need to be ranked, given by four experts. That is, onehas a set of 4 by 20 pay-off distributions. These distributions aregiven in Table 1. The resources to take four best patents into ourportfolio are available.

anking patents

l

Ability to disturb compe�tors act.

Ability to create new markets

anking patents

lAbility to disturbcompe�tors act.

Ability to createnew markets

Ability to protect own

ac�vity

Patent n-1 Patent n. . .

ranking of patents with AHP.



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Table 1Distributions in 10’s of thousands of euro. DM denotes decision-maker.

Patent Min DM1 DM2 DM3 DM4

Bg Max Min Bg Max Min Bg Max Min Bg Max

1 �4.00 4.00 16.00 �3.85 7.00 25.00 �1.00 6.00 19.00 �8.00 6.00 20.002 �2.25 8.00 29.00 �2.50 6.00 22.00 �4.00 14.00 26.00 �3.00 2.00 25.003 �3.25 4.00 12.00 �4.00 5.00 17.00 �3.00 12.00 17.00 �2.00 7.00 13.004 �11.00 9.00 18.00 �9.00 7.00 18.00 �3.00 2.00 15.00 �7.00 7.00 16.005 0.75 2.00 9.00 0.00 3.00 10.00 0.00 5.00 7.00 1.00 2.50 10.006 �8.00 15.00 23.00 �6.00 12.00 28.00 �6.00 20.00 31.00 �5.00 14.00 35.007 �1.50 18.00 35.00 1.00 11.00 31.00 0.00 5.00 27.00 �0.50 15.00 35.008 �1.00 5.00 22.00 �1.75 3.00 27.00 �0.50 11.00 30.00 �1.25 7.00 20.009 �4.00 10.00 18.00 �3.00 8.00 24.00 �3.25 9.00 21.00 �5.00 �1.00 20.0010 5.50 6.00 11.00 2.00 4.00 18.00 1.75 8.00 15.00 3.00 6.00 19.0011 1.00 7.00 27.00 �1.00 2.00 22.00 �1.00 4.00 21.00 0.50 4.00 18.0012 1.75 12.00 14.00 1.00 10.00 20.00 2.00 6.00 22.00 0.50 7.00 15.0013 �2.25 0.00 13.50 �2.00 3.00 15.00 �2.00 11.00 17.00 �1.50 3.00 13.0014 �1.75 8.00 21.00 �1.75 5.00 15.00 �1.00 7.00 17.00 �2.00 9.00 16.0015 0.00 3.00 19.00 1.00 7.00 26.00 0.00 8.00 22.00 �0.25 10.00 23.0016 �0.50 6.00 24.00 �2.00 15.00 34.00 �0.75 15.00 29.00 �1.00 8.00 30.0017 6.00 20.00 33.00 2.00 14.00 30.00 2.50 18.00 40.00 �3.50 22.00 44.0018 �2.75 9.00 30.00 �1.00 11.00 30.00 �2.00 6.00 25.00 �3.00 12.00 27.0019 �3.00 11.00 27.00 �2.50 15.00 31.00 �2.00 16.00 22.00 �3.00 5.00 23.0020 �3.00 9.50 22.00 �1.00 7.00 18.00 �2.00 1.00 14.00 �0.50 1.00 16.00

Table 3Consensus reached for patent 1.

Patent no. 1 dL x dR

DM1 0.1811 0.3045 0.2591DM2 0.1811 0.3045 0.2591DM3 0.1811 0.3045 0.2591DM4 0.1812 0.3046 0.2591



13 March 2013

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These distributions are first scaled between [0,1] and thentransformed into fuzzy numbers of form x = (dL ,x,dR) giving ourdata now in form given in Table 2.

Then the consensus model is applied, this is explained in detailabove in Section 4, to reach a consensus of the four decision mak-ers over the patents. In order to do this the same parameter valuesas in Fedrizzi et al. (2008a, 2008b) are applied, c = 0.005, a = 0.3,b = 10 and k = 0. As an example of the results, Table 3 shows theconsensus reached for the patent (patent 1).

In Fig. 4 one can see the pay-off distributions before and afterthe consensus model was applied for patent 1. Consensus pay-offdistribution for all patents can be seen in Table 4.

Next, the possibilistic moments from the consensus pay-off dis-tributions are calculated for each patent. The moments calculatedinclude the possibilistic mean, the possibilistic standard deviation,and possibilistic skewness of each pay-off distribution. See Section

Table 2Distributions scaled between [0,1] and transformed in the form x = (dL,x,dR).

Patent Min DM1 DM2

Bg Max Min Bg Max

1 0.1455 0.2727 0.2182 0.1973 0.3273 0.32732 0.1864 0.3455 0.3818 0.1545 0.3091 0.29093 0.1318 0.2727 0.1455 0.1636 0.2909 0.21824 0.3636 0.3636 0.1636 0.2909 0.3273 0.20005 0.0227 0.2364 0.1273 0.0545 0.2545 0.12736 0.4182 0.4727 0.1455 0.3273 0.4182 0.29097 0.3545 0.5273 0.3091 0.1818 0.4000 0.36368 0.1091 0.2909 0.3091 0.0864 0.2545 0.43649 0.2545 0.3818 0.1455 0.2000 0.3455 0.290910 0.0091 0.3091 0.0909 0.0364 0.2727 0.254511 0.1091 0.3273 0.3636 0.0545 0.2364 0.363612 0.1864 0.4182 0.0364 0.1636 0.3818 0.181813 0.0409 0.2000 0.2455 0.0909 0.2545 0.218214 0.1773 0.3455 0.2364 0.1227 0.2909 0.181815 0.0545 0.2545 0.2909 0.1091 0.3273 0.345516 0.1182 0.3091 0.3273 0.3091 0.4727 0.345517 0.2545 0.5636 0.2364 0.2182 0.4545 0.290918 0.2136 0.3636 0.3818 0.2182 0.4000 0.345519 0.2545 0.4000 0.2909 0.3182 0.4727 0.290920 0.2273 0.3727 0.2273 0.1455 0.3273 0.2000


5 above for a detailed description. Results for the possibilistic mo-ment calculation for each patent are presented in Table 5.

These possibilistic moments are used in TOPSIS as a three crite-ria ranking problem for getting the patents in a preference order.See Section 5 for a closer description of the TOPSIS method. Calcu-lated closeness coefficients and the resulting ranking order are gi-ven in Table 6.

DM3 DM4

Min Bg Max Min Bg Max

0.1273 0.3091 0.2364 0.2545 0.3091 0.25450.3273 0.4545 0.2182 0.0909 0.2364 0.41820.2727 0.4182 0.0909 0.1636 0.3273 0.10910.0909 0.2364 0.2364 0.2545 0.3273 0.16360.0909 0.2909 0.0364 0.0273 0.2455 0.13640.4727 0.5636 0.2000 0.3455 0.4545 0.38180.0909 0.2909 0.4000 0.2818 0.4727 0.36360.2091 0.4000 0.3455 0.1500 0.3273 0.23640.2227 0.3636 0.2182 0.0727 0.1818 0.38180.1136 0.3455 0.1273 0.0545 0.3091 0.23640.0909 0.2727 0.3091 0.0636 0.2727 0.25450.0727 0.3091 0.2909 0.1182 0.3273 0.14550.2364 0.4000 0.1091 0.0818 0.2545 0.18180.1455 0.3273 0.1818 0.2000 0.3636 0.12730.1455 0.3455 0.2545 0.1864 0.3818 0.23640.2864 0.4727 0.2545 0.1636 0.3455 0.40000.2818 0.5273 0.4000 0.4636 0.6000 0.40000.1455 0.3091 0.3455 0.2727 0.4182 0.27270.3273 0.4909 0.1091 0.1455 0.2909 0.32730.0545 0.2182 0.2364 0.0273 0.2182 0.2727



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0 0.2 0.4 0.6 0.8 10

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1Consensus distributions for patent 1, t=30000

µ(x)

0 0.2 0.4 0.6 0.8 10

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1Scaled distributions for patent 1, t=1

µ(x)

Fig. 4. Scaled pay-off distributions for patent 1. (Left) the four scaled pay-off distributions, one by each decision maker. (Right) The scaled consensus pay-off distribution forpatent 1 after 30000 iterations.

Table 4Consensus distribution for each patent given as a fuzzy number in the formx = (dL, x,dR).

Patent dL x dR

1 0.1811 0.3045 0.25912 0.1898 0.3364 0.32733 0.1829 0.3273 0.14094 0.2501 0.3137 0.19085 0.0488 0.2568 0.10686 0.3910 0.4773 0.25457 0.2274 0.4228 0.35908 0.1386 0.3182 0.33189 0.1876 0.3182 0.259010 0.0534 0.3091 0.177311 0.0796 0.2773 0.322712 0.1353 0.3591 0.163613 0.1124 0.2772 0.188714 0.1614 0.3318 0.181815 0.1238 0.3272 0.281916 0.2193 0.4000 0.331917 0.3046 0.5364 0.331818 0.2125 0.3727 0.336419 0.2613 0.4136 0.254620 0.1137 0.2841 0.2340



13 March 2013

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Now, one can stop here and declare a ranking based on the re-sults from TOPSIS, where patent 7 is the top ranking patent, andfollowed by patents 18,16, and 2 in the top four.

We want to however use more information in the selection pro-cess that is, in addition to the cash-flow data we want to includealso additional (strategic) criteria that we ask three experts to pro-vide. For further analysis the AHP is used and the six best candidatepatents are selected, based on the TOPSIS analysis, from the overalltwenty to be evaluated. The six best patents are: 7,18,16,2,8, and11. The following six criteria are used by the experts to evaluatethe patents:

1. Strategic fit of patent/patent family to the portfolio (balance ofthe portfolio)

2. Technical quality of the patent as seen by the expert3. Licensing (Out/Cross) potential of the patent4. Ability to ‘‘disturb competitors’ activities’’


5. Ability to open new markets/ preparation for the future6. Ability to protect company’s own activity (against others’ IPR)

After the pair-wise comparison of the patents is completed foreach of the criteria the decision makers’ reciprocal matrices areaggregated. This is done by simply using a geometric mean, as iscommonly done in the literature (Xu, 2000). Then we proceed tocalculate priority vectors from the reciprocal matrices. This is doneby calculating normalized principal eigenvectors and by usingthese as priority vectors. The AHP matrices for the pair-wise com-parison of the six criteria can be found in Appendix A. The priorityvectors can be found in Table 7.

Next our attention is turned to the consistency of these resultsand calculate the consistency indexes and the consistency ratiosfor each priority vector, using principal eigenvalues. Results canbe found in Table 8.

As can be seen from Table 8, the consistency ratio is always be-low than 10 %, and from that one can conclude that inconsistency ison a clearly acceptable level. It is assumed here that all criteria areof equal importance and thus they have not been weighted. Next, acomposite vector for each patent is calculated, the results can befound in Table 9. Composite vector in this case is a normalized lin-ear combination of the priority vectors.

From this one can conclude that four selected patents in orderof goodness are: 7, 8, 16, and 2. By comparing the results afterthe AHP one can see that the ranking order of the patents has sig-nificantly changed from the order reached with the TOPSIS analy-sis. Patent number 7 is still the best patent, however with regardsto all the other five patents the order has changed. Inclusion ofadditional strategic information has played a key role in the selec-tion of the four patents from the six (out of the original twenty).

8. Concluding remarks

In this paper, a system for supporting the selection of patents tobe included in a portfolio has been introduced. The system uses atwo-tier decision making process, where two different teams ofagents (experts, decision makers) are involved. The first team iscomposed by experts who are asked to create, independently ofone another, a financial analysis of each patent’s value for the firm



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Table 5Possibilistic moments from the consensus pay-off distributions for each patent.

Patent Mean Standard deviation Skewness

1 0.3175 0.0081 0.00052 0.3593 0.0111 0.00113 0.3203 0.0044 �0.00014 0.3038 0.0081 �0.00045 0.2665 0.0010 0.00006 0.4546 0.0174 �0.00187 0.4447 0.0143 0.00148 0.3504 0.0092 0.00139 0.3301 0.0083 0.000410 0.3297 0.0022 0.000211 0.3178 0.0067 0.001212 0.3638 0.0037 0.000113 0.2900 0.0038 0.000214 0.3352 0.0049 0.000115 0.3536 0.0069 0.000816 0.4187 0.0127 0.001117 0.5409 0.0169 0.000318 0.3934 0.0126 0.001219 0.4125 0.0111 �0.000120 0.3042 0.0050 0.0005

Table 6Closeness coefficient values and the resulting ranking of the patents.

Patent Closeness coefficient Ranking order

1 0.6349 92 0.8072 43 0.4568 184 0.4336 195 0.4675 176 0.3176 207 0.9087 18 0.7930 59 0.6337 1010 0.5179 1411 0.7400 612 0.5069 1613 0.5303 1314 0.5141 1515 0.6925 816 0.8343 317 0.7090 718 0.8407 219 0.5512 1220 0.5951 11

Table 7The priority vectors for each six criteria.

Priorityvector 1

Priorityvector 2

Priorityvector 3

Priorityvector 4

Priorityvector 5

Priorityvector 6

Patent2

0.1803 0.1273 0.1358 0.1256 0.1277 0.1324

Patent7

0.1541 0.3753 0.2330 0.1588 0.1640 0.3825

Patent8

0.2145 0.0996 0.1373 0.3278 0.1232 0.1712

Patent11

0.1431 0.1453 0.1418 0.1077 0.1277 0.1250

Patent16

0.2244 0.1406 0.2381 0.1559 0.1277 0.1247

Patent18

0.0837 0.1119 0.1140 0.1242 0.3298 0.0642

Table 8Consistency indexes (CI) and consistency ratios (CR) for the six priority vectors.

Priorityvectors

Priorityvector 1

Priorityvector 2

Priorityvector 3

Priorityvector 4

Priorityvector 5

Priorityvector 6

CI 0.002 0.0039 0.0032 0.0156 0.002 0.0039CR 0.0016 0.0031 0.0026 0.0126 0.0016 0.0032

Table 9Composite priority vectors for the patents and the ranking of the patents, based onthe composite priority vector.

Patent no Composite Ranking

Patent 2 0.1382 4Patent 7 0.2446 1Patent 8 0.1789 2Patent 11 0.1318 6Patent 16 0.1686 3Patent 18 0.1380 5



13 March 2013

Q1

by using three value scenarios. These scenarios are then used tocreate individual fuzzy pay-off distribution functions that are rep-resented as triangular fuzzy numbers.

Then, a dynamic consensus reaching mechanism is introducedto determine, for each patent, the group fuzzy pay-off distribu-tion that is, a consensual triangular fuzzy number. Three possibi-listic moments are calculated from the consensual pay-offdistributions for each patent. These are used in a first rankingof patents that is obtained by using the TOPSIS method. The sec-ond team of ‘‘elected’’ decision-makers performs an AHP process,based on relevant strategic criteria, to create the final ranking ofthe patents that can be used in supporting the patent portfolioselection.

In Section 7, a numerical example was introduced to show howthe system works in practice, and how the introduction of addi-


tional analysis with AHP based on six additional criteria has chan-ged the ranking order of the patents. The numerical analysis hasbeen done with Matlab.

The most remarkable novelty of our approach consists in pro-posing a mixed procedure which permits to combine technicalvaluation and ranking of patents, as carried out by a team of ex-perts focused on more accounting-based attributes, with a stra-tegic evaluation that takes care of the scenario factorscharacterizing the global competitive market including, forexample scope and coverage, product marketplace value, anddefensive and offensive potential. The usability of the systemproposed here is by no means limited to the valuation of pat-ents. It can be used for any similar problems where the rankingof competing assets benefit from performing both financial and‘‘strategic’’ analysis, such as for example ranking of R&D projects.

In the future, we will extend the model introducing linguisti-cally-based descriptions of attributes’ values in the TOPSIS rankingand in the AHP process as well and a fuzzy rule-based frameworkto make more effective the representation of experts’ knowledge.We aim to look also at the relationship between some financialmeasures such as the real option value and the possibilisticmoments.



Appendix A. The AHP matrixes for the pair-wise comparison of the six criteria

DM1 DM2 DM3

Criteria 1 2 7 8 11 16 18 Criteria 1 2 7 8 11 16 18 Criteria 1 2 7 8 11 16 182 1.00 2.00 0.50 1.00 0.50 5.00 2 1.00 1.00 1.00 1.00 1.00 2.00 2 1.00 1.00 1.00 2.00 1.00 1.007 0.50 1.00 0.25 0.50 0.25 3.00 7 1.00 1.00 2.00 1.00 1.00 3.00 7 1.00 1.00 1.00 2.00 1.00 1.008 2.00 4.00 1.00 2.00 1.00 7.00 8 1.00 0.50 1.00 1.00 1.00 2.00 8 1.00 1.00 1.00 2.00 1.00 1.0011 1.00 2.00 0.50 1.00 0.50 5.00 11 1.00 1.00 1.00 1.00 1.00 2.00 11 0.50 0.50 0.50 1.00 0.50 0.5016 2.00 4.00 1.00 2.00 1.00 8.00 16 1.00 1.00 1.00 1.00 1.00 2.00 16 1.00 1.00 1.00 2.00 1.00 1.0018 0.20 0.33 0.14 0.20 0.13 1.00 18 0.50 0.33 0.50 0.50 0.50 1.00 18 1.00 1.00 1.00 2.00 1.00 1.00






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References

Agliardi, E., & Agliardi, R. (2011). An application of fuzzy methods to evaluate apatent under the chance of litigation. Expert Systems with Applications, 38,13143–13148.

Brunelli, M., Fedrizzi, M., Fedrizzi, R., & Marques Pereira, R. A. (2010). The dynamicsof consensus in group decision making: investigating the pairwise interactionsbetween fuzzy preferences. In S. Greco, R. A. Marques Pereira, M. Squillante, R.Yager, & J. kacprzyk (Eds.), Preferences and decisions: Models and applications. NY:Springer.

Cabrerizo, F. J., Moreno, J. M., Perez, E., & Herrera-Viedma, E. (2010). Analyzingconsensus approaches in fuzzy group decison making: advantages anddrawbacks. Soft Computing, 14, 451–463.

Camus, C., & Brancaleon, R. (2003). Intellectual assets management: from patents toknowledge. World Patent Information, 25, 155–159.

Carlsson, C., & Fullér, R. (2001). On possibilistic mean value and variance of fuzzynumbers. Fuzzy Sets and Systems, 122, 315–326.

Carlsson, C., Fuller, R., Heikkilä, M., & Majlender, P. (2007). A fuzzy approach to R&Dproject portfolio selection. International Journal of Approximate Reasoning, 44,93–105.

Collan, M. (2010). A DSS for supporting area development decision-making. In IEEEInternational Conference on Information Management and Engineering. Chengdu,PRC: IEEE.

Collan, M. (2011). Valuation of industrial giga-investments: Theory and practice.Fuzzy Economic Review, XVI.

Collan, M. (2012). The pay-off method: Re-inventing investment analysis. Charleston,NC, USA: CreateSpace Inc..

Collan, M., Fuller, R., Mezei, J., & Wang, X. (2011). Numerical patent analysis withthe fuzzy pay-off method: valuing a compound real option. In IEEE 4thinternational conference on business intelligence and financial engineering(BIFE 2011). Wuhan, PRC.

Collan, M., Fullér, R., & Mezei, J. (2009a). A fuzzy pay-off method for real optionvaluation. In IEEE international conference on business intelligence and financialengineering (pp. 165–169). Beijing, PRC: IEEE.

Collan, M., Fullér, R., & Mézei, J. (2009b). Fuzzy pay-off method for real optionvaluation. Journal of Applied Mathematics and Decision Systems, 20.

Collan, M., & Heikkilä, M. (2011). Enhancing patent valuation with the pay-offmethod. Journal of Intellectual Property Rights, 16, 377–384.

Collan, M., & Kinnunen, J. (2011). A procedure for the rapid pre-acquisitionscreening of target companies using the pay-off method for real optionvaluation. Journal of Real Options and Strategy, 4, 115–139.

Fedrizzi, M., Fedrizzi, M., Pereira, R. A. M., & Brunelli, M. (2008). Dynamics in groupdecision making with triangular fuzzy numbers. In: HICSS. Hawaii, USA.

Fedrizzi, M., Fedrizzi, M., Pereira, R.A. M ., & Brunelli, M. (2008). Consensualdynamics in group decision making with triangular fuzzy numbers. In HICSS 41.Hawaii, USA.

Fedrizzi, M., Fedrizzi, M., & marques Pereira, R. A. (1999). Soft consensus andnetwork dynamics in group decision making. International Journal of IntelligentSystems, 14, 63–77.

Fedrizzi, M., Fedrizzi, M., & Marques Pereira, R. A. (2007). Consensus modelling ingroup decision making: a dynamical approach based on fuzzy preferences. NewMathematics and Natural Computation, 3, 219–237.

851


Fuller, R., & Majlender, P. (2003). On weighted possibilistic mean and variance offuzzy numbers. Fuzzy Sets and Systems, 136, 363–374.

Grzegorzewski, P. (1998). Metrics and orders in space of fuzzy numbers. Fuzzy Setsand Systems, 97, 83–94.

Hassanzadeh, F., Collan, M., & Modarres, M. (2012). A practical approach to R&Dportfolio selection using fuzzy set theory. IEEE Transactions on Fuzzy Systems, 20,615–622.

Huang, C.-C., Liang, W.-Y., Lin, S.-H., Tseng, T.-L., & Chiang, H.-Y. (2011). A rough setbased approach to patent development with the consideration of resourceallocation. Expert Systems with Aplications, 38, 1980–1992.

Hwang, C.-L., & Yoon, K. (1981). Multiple attributes decision making methods andapplications. Berlin: Springer, Heidelberg.

Jain, A., Murty, M., & Flynn, P. (1999). Data clustering: A review. ACM ComputingSurveys, 31, 265–323.

Karsak, E. (2006). A generalized fuzzy optimization framework for R&D projectselection using real options valuation. In M. e. A. Gavrilova (Ed.), Computationalscience and its applications – ICCSA 2006 (pp. 918–927). Berlin Heidelberg:Springer-Verlag.

Kaufman, M., & Gupta, M. (1991). Introduction to fuzzy arithmetic. New York, NY:Van Nostrand Reinhold.

Littman-Hillmer, G., & Kuckartz, M. (2009). SME tailor-designed patent portfolioanalysis. World Patent Information, 31, 273–277.

Mathews, S., & Salmon, J. (2007). Business engineering: A practical approach tovaluing high-risk, high-return projects using real options. In P. Gray (Ed.),Tutorials in Operations Research: Informs.

Mathews, S., & Datar, V. (2007). A practical method for valuing real options: Theboeing approach. Journal of Applied Corporate Finance, 19, 95–104.

Park, H., Kim, K., Choi, S., & Yoon, J. (in press). A patent intelligence system forstrategic technology planning. Expert Systems with Applications.

Reilly, R. F., & Schweihs, R. P. (1998). Valuing intangible assets. Blacklick, OH, USA:McGraw-Hill Professional Publishing.

Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journalof Mathematical Psychology, 15, 234–281.

Saaty, T. L. (1980). The analytic hierarchy process. New York, NY: McGraw-Hill.Saaty, T. L. (1986). Axiomatic foundation of the analytic hierarchy process.

Management Science, 32, 841–855.Saaty, T. L. (1987). The analytic hierarchy process: What is and how it is used.

Mathematical Modelling, 9, 161–176.Smith, G. V., & Parr, R. (2000). Valuation of intellectual property and intangible assets.

New York: John Wiley & Sons.Tran, L., & Duckstein, L. (2002). Comparison of fuzzy numbers using a fuzzy distance

measure. Fuzzy Sets and Systems, 130.van Triest, S., & Vis, W. (2007). Valuing patents on cost-reducing technology: A case

study. International Journal of Production Economics, 105, 282–292.Voxman, W. (1997). Some remarks on distances between fuzzy numbers. Fuzzy Sets

and Systems, 100, 353–365.Xu, Z. (2000). On consistency of the weighted geometric mean complex judgment

matrix in AHP. European Journal of Operational Research, 126, 683–687.Zadeh, L. A. (1975). The concept of a linguistic variable and its application to

approximate reasoning I–II–III. Information Sciences (pp. 199–249, 301–357,143–180).

Zadeh, L. A. (1983). A computational approach to fuzzy quantifiers in naturallanguages. Computer Mathematics with Applications, 9, 149–183.



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