EXPERTISE-BASED EXPERTS IMPORTANCE WEIGHTS IN ADVERSE JUDGMENT

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1 VOL. 9, NO. 9, SEPTEMBER 04 ISSN ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Network (ARPN). All rights reserved. EXPERTISE-BASED EXPERTS IMPORTANCE WEIGHTS IN ADVERSE JUDGMENT Evy Herowati,, Udisubakti Ciptomulyoo, Joiarto Parug ad Suparo Idustrial Egieerig, Istitute of Techology Sepuluh Nopember, Surabaya, Idoesia Idustrial Egieerig, Uiversity of Surabaya, Surabaya, Idoesia ABSTRACT The obective of this research was to propose the use of expertise levels of experts to determie the experts importace weights sice there has bee o research that determies the 'importace weight' usig the expertise level as a whole. The sigificace of this research was the itegratio of three cocepts, amely: the expert s expertise level, FPR s Additive Cosistecy ad the Iduced-OWA operator to obtai the expert s importace weight i adverse udgmet situatio. The Expertise level of a expert i adverse udgmet situatio is determied by his/her ow assessmet o a set of alteratives ad defied as the ability to differetiate cosistetly ad expressed as the ratio betwee Discrimiatio ad Icosistecy. The experts provided their prefereces usig FPR (Fuzzy Preferece Relatios) sice FPR has Additive Cosistecy property to replicate each elemet of FPR matrix. Experts were sorted accordig to their expertise level ad the experts importace weights followed the OWA (Ordered Weighted Averagig) operator s weights which were determied by parameterizatio usig Basic Uit-Iterval Icreasig Mootoic fuctios. The experts importace weights model illustrated by a umerical example, ad it cocluded that the higher the expert s expertise level, the higher his/her importace weight. Keywords: additive cosistecy, expertise, fuzzy preferece relatios, importace weight, iduced OWA operator. INTRODUCTION The expertise level of decisio maker greatly affects the quality of the resultig decisio []. The decisio quality made by the experts presumed better tha decisio quality made by the o-experts as a expert have the ability to th differetly [-3]. This is because the iheret ability of the experts eables them to uderstad problems i more detail ad depth so that the experts ca distiguish the various aspects of the situatio that is usually overlooked by the o-expert [4]. Related to decisio that requires the Decisio Maker (DM) expertise i Group Decisio Makig (Decisio Makig with more tha oe DM), the DM idividual assessmet eeds to be explored ad group decisio is take based o the itegratio of idividual assessmets ito the group assessmet, by performig aggregatio of DM assessmets mathematically [5]. Oe importat factor that must be cosidered i the aggregatio process is the importace weight of each DM. The magitude of the DM s importace weight ifluece decisios. If a DM assessig a alterative with a high score ad this DM gets a high importace weight, the this alterative would get a high total score ad most lely has a high opportuity to be selected as the best alterative. Therefore, to improve the decisio quality, the DMs importace weights should be determied based o their expertise level. Some researchers defied the expertise level as "the ability to differetiate cosistetly" through the evaluatio of his/her assessmet level o alteratives [6-7]. The level assessmet o alteratives is called the adverse udgmet [8]. Shateau (00) stated the experts as those who ca differetiate betwee similar but ot exactly the same, cases ad repeat their assessmets cosistetly. They formulated the expertise level as the ratio betwee Discrimiatio ability ad Icosistecy [6-7]. The drawback of this formulatio foud i the Icosistecy measuremet [9]. Measurig Icosistecy required repetitio; cosequetly the experts eed to assess the same cases more tha oce. Assessig the same cases more tha oce is very difficult to do idepedetly without beig iflueced by previous assessmets. This is the reaso of the eed for adustmet to the formula implemetatio i determiig the expertise level. A umber of researches have bee proposed i determiig the DMs importace weights ad ca be categorized ito groups: direct evaluatio to DMs ad evaluatio to the DMs assessmet level. The DMs importace weights determiatio through direct evaluatio to DMs cosists of a supra DM' who assessed the DM the gave weight to each DM [0-] ad 'a group of DM' who assessed each member i the DM group [3-5]. The direct evaluatio methods could potetially lead to decisio bias due to the assessors subectivity, the assessors difficulty i assessig other DM ad popularity effect (a perso who has bee recogized by peers usually assumed more expert; but it is possible that the assumed less expert would be the creator of ew kowledge [6]). While the determiatio of the DMs importace weight through evaluatio of their assessmet o a set of alteratives ca be classified ito the determiatio of importace weights based o maximum cosesus that could be achieved i the group [6-8], miimum deviatio of DM idividual opiio to the group opiio [9-], miimum distace from the DM idividual opiio to group opiio [-7] ad cosistecy of DM assessmet o alteratives [8, 8-30]. I geeral, the methods of determiig the DM importace weights i the 48

2 VOL. 9, NO. 9, SEPTEMBER 04 ISSN ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Network (ARPN). All rights reserved. adverse udgmet situatio are more obective tha direct evaluatio to the DMs. These methods had certai property: the closer the DM s idividual opiio o group average opiio, the greater his/her importace weight regardless of his/her expertise level. I particular, there were methods of importace weight determiatio based o the DM s cosistecy evaluatio i pairwise compariso FPR (Fuzzy Preferece Relatio). These methods assumed that the more cosistet the DM prefereces, the more relevat the DM opiio ad resultig the higher the DM importace weight. These cosistecy-based methods are more obective compared with the other methods, but these methods have ot cosidered the expertise level as a whole. I this paper, the DM importace weight is determied based o the expertise level as a whole as the ability to differetiate cosistetly ad expressed by the ratio betwee Discrimiatio ad Icosistecy ad the difficulty i repetitio is replaced by estimatio usig Additive Cosistecy (AC) of FPR. The DM provides preferece i the form of pairwise comparisos FPR where FPR has the Additive Cosistecy (AC) properties that used to estimate repetitio. The experts the sorted by their expertise level ad the experts importace weights are associated with the OWA (Ordered Weighted Averagig) operator s weights which are determied by parameterizatio usig Basic Uit-Iterval Icreasig Mootoic fuctios (BUM). To do this, this paper is orgaised as follows. Followig the first Sectio, it is discussed the cocepts used to obtai the DM s Importace weight, amely the expertise level of expert, the AC property of FPR ad the Iduced OWA Operator. Next, the methodology to obtai the expertise-based experts importace weights is discussed ad followed by the applicability test of the methodology usig a umerical example. Fially, i the last Sectio we drew our coclusios. LITERATURE REVIEWS There are three importat cocepts used i this research to obtai the DM s Importace weight, amely the experts expertise level, the AC property of FPR ad the Iduced OWA Operator. The Expertise Level of Experts A expert usually has some backgrouds i certai fields ad recogized by his/her peers [3]. Shateau et al. (00) determie the expertise level of a expert based o his/her assessmet level (adverse udgmet). They argued that oly people who ca differetiate betwee similar but ot exactly the same, cases ad repeat their udgmet cosistetly, cosidered as a expert [6]. Therefore there are two requiremets ecessary for determiig the expertise level, amely the Discrimiatio ability ad the Icosistecy ad expressed i CWS - Idex as show i eq (), () ad (3): Discrimiatio CWS -Idex = Icosistesy stadard deviatio of differet alteratives' values = () stadard deviatio of the same alterative's values Discrimiatio= Icosistecy= r( M GM ) = r ( M i M ) = = ( r ) () i (3) Where r : The umber of replicatios M : The average of idividual values for case- GM : Grad mea of all idividual values : The umber of differet cases M i : The idividual value for replicatio-i case- I order to measure the expertise level of the experts, the evaluated experts were asked to elicitate their evaluatio more tha oce. Oly those who have a high level of Discrimiatio ability ad low level of Icosistecy ca be clasified as expert ad obtai a high value of CWS-Idex. Ufortuately, this method required repetitio ad this repetitio are very hard to do idepedetly without beig affected by previous evaluatio. The Additive Cosistecy of FPR The Decisio Makers could use a variety of evaluatio formats, amog others, is FPR. FPR is oe of the most widely used evaluatio format to provide evaluatio i Group Decisio Makig (GDM) [6, 3-33] sice FPR ca be used as tools o aggregatig idividual opiios ito a group opiio [34]. Suppose that a group of Decisio Makers E = { e, e,... em }, m evaluate a fiite set of alteratives X = { x, x,... x}, by usig pairwise comparisos FPR P XxX havig a membership fuctio µ p : XxX [0,] ad represeted by meas of the x matrix P = ( pi ) [35]. p is the preferece degree of i alterative xi over x. p = i meas idifferece betwee xi ad x, p > meas x i i is preferred to AC property of FPR amog three alteratives x ad x k [36] are as follows: ( p 0,5) + ( p 0,5) = ( p 0,5) p i i k + p k + pki = 3 x. x i, i,, k =,,..., (4) i,, k =,,..., (5) 49

3 VOL. 9, NO. 9, SEPTEMBER 04 ISSN ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Network (ARPN). All rights reserved. The AC property yields a relatioship betwee the prefereces ad we ca obtai estimated values by usig 3 differet formulas as follows [8]: ε p, i, k (6) = pi + p k = p k p i ε p +, i, k (7) ε p +, i, k (8) 3 = pi pk i which: ε p : Estimatio of p usig the first formula ε p : Estimatio of p usig the secod formula 3 ε p : Estimatio of p usig the third formula For every elemet of the matrix FPR p i, these formulas produce as may as 3x (-) replicatios (sice there are 3 formulas ad i, k ). These replicatios allow AC property be used to complete the icomplete FPR [8-9, 37-4] ad measure someoe's cosistecy level i providig assessmet [8-9, 34, 39-40, 4] i which the cosistecy level the be used to determie the importace weight of each expert. The drawbacks are previous studies oly cosidered the Cosistecy level, but ot the Discrimiatio, thus have ot covered the whole cocept of expertise level as proposed by Shateau et al., (00). The Iduced OWA Operator The OWA operator is a aggregatio operator proposed by Yager (988) i which the order of the argumets have primary role i the aggregatio process [43]. A -dimesioal OWA Operator is a mappig F I : I defied as Fw ( a, a,..., a ) = w b where = b is the th largest elemet i the set of iput argumets ( a, a,..., a) ad w is the order weights satisfy w 0 ad w = [43]. I this case the iput = argumets are ordered accordig to their ow values. I the Iduced OWA Operator, the orderig of the iput argumets are based upo the order iducig variable [44]. A dimesioal Iduced OWA Operator Is a mappig F : I I defied as Fw ( u, a, u, a,..., u, a ) = w b where u i is = called the order iducig variable ad a i is called iput argumet, w is the order weights ad w 0 ad w = ad b is the iput argumet value of the pair = havig the -th largest value for the order iducig variable. A importat issue i usig the OWA operator or the Iduced OWA operators i aggregatio process is the issue of obtaiig the OWA weights. Yager (996) proposed that the OWA weights ca be parameterized by BUM Q : [0,] [0,] havig the properties: Q( 0) = 0; Q() = ; Q( x) Q( y) if x y ad the OWA weights w are as follows [45-46]: ( ) Q( R ) = Q R w (9) where R > R, ad the obtaied weights satisfy w 0 ad w =. The BUM is associated with the = accumulatio of DM importace weight. Sice BUM is a icreasig Mootoic Fuctio as illustrated i Figure-, the the idividual DM importace weight ca t be egative or w 0. Aother importat property of this fuctio is the maximum value of BUM is oe, so the accumulatio of the total DM importace weights also. Yager (988) proposed a particular form of BUM Fuctio as α = R, α positive parameter [43]. Figure-. The OWA Weights from Basic Uit Iterval Icreasig Mootoic Fuctio. THE PROPOSED METHOD This research uses expertise level as the ability to differetiate cosistetly ad expressed as ratio betwee Discrimiatio ad Icosistecy ad the experts provide evaluatio usig pairwise compariso FPR. AC property of FPR eables us to get the replicatios without askig the DMs to repeat their evaluatio ad the result of this step is CWS-Idex. Based o this Idex, we obtai the rak of the DMs based o their assessmet level [9, 47]. The ext step is obtaiig the DMs importace weights based o the Iduced OWA weights ad BUM fuctio as illustrated i Figure-. The expertise-level expressed by the CWS-Idex i logarithmic fuctio ad used as the order iducig variable. The expertise-level are used as the R-variable i determied the importace weights. NUMERICAL EXAMPLE I order to show the applicability of the proposed methods, we provide a umerical example to illustrate 430

4 VOL. 9, NO. 9, SEPTEMBER 04 ISSN ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Network (ARPN). All rights reserved. Expertise-based experts importace weight. Suppose there are 5 experts expressed i E = e, e, e, e, } ad { 3 4 e5 asked to provide assessmet o a set of 4 alteratives X = { x, x, x3, x4}. The data of experts assessmet are as follows [47]: Figure-. The Proposed Method P =, P = 3, P =, P = , value ad we ca calculate Discrimiatio ad Icosistecy value. Discrimiatio= Icosistecy = r( M GM ) = = = ( ) r = = ( M i M ) i = = 0.97 ( r ) x(7 ) P = The estimatio of each matrix elemet by usig formula, ad 3 will geerate 6 estimated values. For example the estimated value of all matrix P 4 elemets is preseted i Table-. For each elemet of the matrix P 4 there are 7 values (r = 7), i.e. 6 estimated values ad real CWS-Idex for Expert 4 = = The CWS-idex for all experts are represeted i Table-. CWS-Idex for Expert-, Expert-, Expert-3, Expert-4 ad Expert-5 subsequetly is 3.580, 8.37,.60,.69 ad 7.6. Based o these CWS-Idexes, the Expertise-based Experts rakig obtaied is [47]: Expert

5 VOL. 9, NO. 9, SEPTEMBER 04 ISSN ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Network (ARPN). All rights reserved. Table-. The CWS-Idex calculatio for Expert-4. r Elemet Origial Formula- Formula- Formula-3 M r( M GM ) ( M i M ) Matrix data i= p p p p p p p p p p p p Total Table-. Discrimiatio, Icosistecy, CWS-Idex ad Experts Rakig. e e e 3 e 4 e 5 Discrimiatio Icosistecy CWS-Idex Rak Table-3. The Importace Weights Calculatio Usig BUM = R. e 3 e e 5 e e 4 CWS- Idex,600 8,370 7,60 3,5800,690 Log(CWS-Idex),007 0,958 0,885 0,5539 0,9 Accumulated(Log(CWS-Idex)),007,065,8980 3,459 3,6638 R=Normalized(Accumulated(Log(CWS-Idex)) 0,3004 0,5504 0,790 0,94, R = R = α 0,7403 0,863 0,943 0,985,0000 Importace Weights for α = 0. 5 (i %) 74,03,0 8,7 4,, R = R = α 0,548 0,749 0,8894 0,9706,0000 Importace Weights for α = 0. 5 (i %) 54,8 9,38 4,75 8,3,94 = R α = R 0,3004 0,5504 0,790 0,94,0000 Importace Weights forα = (i %) 30,04 5,00 4,06 5, 5,78 R = R = α 0,0903 0,309 0,656 0,8877,0000 Importace Weights for α = (i %) 9,03,7 3,7 6,0,3 α Table-3 shows the importace weights α calculatio usig BUM = R. After obtaiig the rak, the experts are sorted by their expertise level. Expert-3 ( e 3 ) is a expert with the highest rak ad placed o the first order. Expert- ( e 3 ) is i the secod order. The we calculate the logarithm of the CWS-Idex ad the accumulatio of the logarithm of the CWS-Idex. After ormalized the accumulatio of the logarithm of the CWS- Idex, the maximum value of these logarithm is i accordace with the BUM fuctio which has a maximum value of ad the experts total Importace weights are. I Table-3, the BUM fuctio will be determied by 43

6 VOL. 9, NO. 9, SEPTEMBER 04 ISSN ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Network (ARPN). All rights reserved. several values of the parameter α. For example, for the parameters α = 0. 5, α = 0. 5, α =, α =. Suppose, we wat to determie the importace weight of DMs for parameter α = The CWS-Idex for e 3 is,60 For e 3, Log(CWS-Idex)=log(,60) =,007 For e, Log(CWS-Idex)=log(8,370 = 0,958 For e 3, Acc((Log(CWS-Idex)) =,007 For e,acc((log(cws-idex)) =,007+0,958=,065 For e 3,R=Norm(Acc(Log(CWS-Idex)))=,007/3,6638= 0,3004 For e,r=acc((log(cws-idex))=,065/3,6638 = 0, If parameter α = 0, 5, = R α = R 0.5 For e 3, Q (0,3004) = 0,3004 = 0, For e, Q (0,3004) = 0,5504 = 0, 863 The Importace weight for e 3 is 74, 05 %. The Importace weight for e is 86, 3% - 74, 05 % =, 0 % If parameter α =, mismatches occur sice the expert with higher expertise level gaied smaller importace weight, for example Expert-3 ( e 3 ) as the expert with the highest expertise level, gets the smallest importace weight. If the parameter α =, expert with higher level of expertise gaied greater importace weight but ot sigificatly. If the parameter α = 0. 5, expert with higher level of expertise gaied greater importace weight sigificatly. Thus the parameter α should be less tha to obtai the expected result, the higher the expert s expertise level, the higher his/her importace weight. CONCLUSIONS A expertise-based experts importace weight method is proposed i order to develop the experts importace weight i adverse udgmet situatio i which every expert provides his/her udgmet i pairwise comparisos FPR. This model cosists of stages. The first stage, we obtai the experts rakig by combiig the experts expertise level ad Additive Cosistecy of FPR. I the secod stage, we develop the experts importace weight by usig Basic Uit-Iterval Icreasig Mootoic α Fuctios = R, α < to get the expected results, the higher the expert s expertise level, the higher his/her importace weight. ACKNOWLEDGEMENTS Preparatio of this paper was supported, i part, by the fiacig of Research Grats for Private Uiversity Lecturer i Kopertis Regio 7, Fiscal Year 04, No. 004/SPH/P/K7/KM/04, April 3, 04 issued by Miistry of Educatio ad Culture, Directorate Geeral of Higher Educatio ad the Research Fudig issued by Uiversity of Surabaya. REFERENCES [] V. Malhotra, M. D. Lee ad A. Khuraa Domai experts ifluece decisio quality: Towards a robust method for their idetificatio. Joural of Petroleum Sciece ad Egieerig. 57(-): [] M. T. H. Chi, R. Glaser ad M. J. Farr The Nature of Expertise. New Jersey. Lawrece Erlbaum Associates. [3] J. R. Aderso Cogitive Psychology ad its Implicatios. Vol. 5. New York: Worth Publishig. [4] C. Hor How experiece affects perceptio i Expert Decisio-Makig. Perceptio (): -0. [5] R. M. Cooke. 99. Experts i ucertaity. Opiio ad subective probability i sciece. New York/Oxford: Oxford Uiversity Press. [6] J. Shateau, D. J. Weiss, R. P. Thomas ad J. C. Pouds. 00. Performace-based assessmet of expertise: How to decide if someoe is a expert or ot? Europea Joural of Operatioal Research. 36(): [7] D. J. Weiss ad J. Shateau Empirical Assessmet of Expertise. Huma Factors. 45(): [8] C. Ya, L. Jig, C. Xia ad L. Yuayua Method o the Assessmet Level of Experts i Group Decisio Makig Based o Multi-graularity Liguistic Judgmet Matrices. I Iformatio Egieerig ad Computer Sciece. Wuha. pp. -5. [9] E. Herowati, U. Ciptomulyoo, J. Parug ad Suparo. 03. Competet-based Experts Rakig at Fuzzy Preferece Relatios o Alteratives. I Iteratioal Coferece o Idustrial Egieerig ad Service Sciece, Surabaya, Idoesia, pp. K7.- K7.6. [0] R. L. Keeey A group preferece axiomatizatio with cardial utility. Maagemet Sciece. 3(): [] F. Herrera, E. Herrera-Viedma ad J. L. Verdegay Choice Processes for No-Homogeeous Group Decisio Makig i Liguistic Settig. Fuzzy Sets ad System. 94(3): [] E. Charmela, J. Parug ad E. Herowati Pegembaga Model Itegrasi Iformasi Subektif da Obektif pada Multiple Attribute Group Decisio Makig. Joural of Logistics ad Supply Chai Maagemet. ():

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