The usability study details initial testing of the GIMCF-AHP prototype in a practical MADM task or environment.

Transcription

1 Interctive Web-bsed Anlyticl Hierrchy Process Group Decision Support System Wddh H. Ftny, The School of Computer Science, the University of Mnchester Abstrct This study dels ith the usbility of ne eb bsed group decision support system. The Group Interctive Modified Compenstory Fuzzy Anlyticl Hierrchy Process (GIMCF-AHP) progrm implements three phse interctive group decision mking process to solve multi-ttribute decision mking (MADM) problems. In the first phse, n (IMCF-AHP) progrm (Ftny 007) is used to elicit rnking of criteri; in the second phse the (IMCF-AHP) progrm is used to elicit eights; nd in the third phse the (IMCF-AHP) progrm is used to collect evlutions to form n overll group preference. The GIMCF-AHP progrm complements the (IMCF-AHP) progrm. The purpose of the to eb bsed progrms is to promote more efficient (i.e. time, cost nd effort) nd effective (i.e. qulity, ccurcy, robustness) decision mking in eb environment. Existing decision support systems re often described s being unttrctive (Aloysius, Dvis et l. 006). The to eb progrms re implemented through client-side dynmic html code (i.e. Html, JvScript, DOM, nd CSS). Client side code execute fster thn server-side code. With the dvent of the Ajx frmeork the client-side coding of eb pplictions hs gined more significnce. The centrl ttrctive feture of the progrm is the implementtion of n itertive group interction process. The lrge MADM problem is decomposed into series of smll problems. The solution of the smll problem my be enough to solve the lrge problem from single decision mker s point of vie, but ll group members need to prticipte in the decision mking process. The phsed interctive group decision mking process llos group members to prticipte in decision mking in unique mnner. Every phse consists of set of rounds. Every round, initited by click on n element on the min eb pge, results in the lunching of ne eb form to collect user input. Every round results in the solution of the problem from different ngle. The min eb pge collects the outcomes from the different rounds nd displys the consensus rnks, eights or evlutions. The multiple solutions nd viepoints contribute to more robust solution nd more effective decision mking process. The usbility study detils initil testing of the GIMCF-AHP prototype in prcticl MADM tsk or environment.

2 1. Introduction A Decision Support System (DSS) is softre rtefct developed to support decision mking. A Web Decision Support System (WDSS) is DSS designed to support decision mking in eb environment. A Group Decision Support System (GDSS) is DSS designed to support group decision mking. As more products nd services become vilble on the internet, better decision support tools re needed to help groups nd individuls mke better decisions (i.e. mke trde-offs beteen different criteri nd lterntives nd select the best choice). DSS re needed on the eb to help groups nd individuls cope ith informtion overlod nd to be ble to process lrge mounts of dt in short period of time. This pper describes ne eb bsed group decision support system bsed on the Anlyticl Hierrchy Process (AHP) model (Sty 1987). Although the AHP model hs been idely utilized in mny different pplictions nd fields, the model hs its critics. Our min concern in this study is ith the redesign of the AHP in order to fcilitte better usbility of the model in eb environment. We consider usbility of WDSS to be dependent on to issues: decision mking efficiency, nd decision mking effectiveness. The to issues re often conflicting system gols. To improve the qulity, comprehensiveness or robustness of decision (i.e. decision mking effectiveness), more time nd effort re required (i.e. decision mking efficiency is scrificed), nd vice vers. Different decision support tools must therefore be developed to del ith different requirements nd circumstnces. Tking these to issues into considertion, e developed the Interctive Modified Compenstory Fuzzy Anlyticl Hierrchy Process (IMCF-AHP), nd the Group (GIMCF-AHP) models. This pper is orgnized s follos. In section e describe the theoreticl foundtion of the AHP nd describe the modifictions introduced by the IMCF-AHP model (Ftny 007) to promote more efficient decision mking in eb environment. In section 3 e discuss group decision mking nd describe the GIMCF-AHP model nd the concept of rounds hierrchy hich e use to fcilitte more effective group decision mking process. In section 4 e describe eb ppliction here the GIMCF-AHP prototype is implemented to test the usbility of the model in decision mking scenrio.. Theoreticl Foundtion of the AHP nd IMCF-AHP models The mthemticl foundtion of the AHP is bsed on the eigenvector method (EM) developed by (Sty 1977; Sty 1978; Sty nd Vrgs 1984; Sty 1987; Sty 1990; Sty 1990; Sty 1994; Sty nd Hu 1998; Sty 003; Sty nd Ozdemir 003). The lgorithm provides mechnism for: - Hierrchicl Structuring; - Preference Elicittion; - Construction of vlue function to represent user preferences; nd - Mesuring Consistency of user s judgments

3 Hierrchicl structuring refers to the decomposition of decision function into lyers. The decision function in the top lyer is dependent on the vlue of the function in the loer lyers. Preference Elicittion refers to the mode in hich the user's preferences re collected nd interpreted. The procedure for Preference Elicittion used by the AHP is pir-ise comprison. The procedure consists of sking the user to systemticlly mke pir-ise comprisons beteen different fctors t ech level in the hierrchy. The user is sked to mke numericl ssignment bsed on pir-ise comprisons for ech lyer in the hierrchy ccording to the guidelines in Tble 1. Tble 1: Guidelines for Pir-ise comprisons User's subjective ssessment of the importnce of fctors in the hierrchy Fctor i nd j re of equl importnce 1 Fctors i is ekly more importnt thn j 3 Fctors i is strongly more importnt thn j 5 Fctors i is very strongly more importnt thn j 7 Fctors i is bsolutely more importnt thn j 9 Numericl Assignment Intermedite vlues,4,6,8 Fctor j is ekly more importnt thn i 1/3 Fctor j is strongly more importnt thn i 1/5. User's subjective ssessments re orgnized in reciprocl mtrix [A], composed of the elements ij. Ech element ij is numericl ssignment of judgement involving to fctors in the sme lyer. The reciprocl mtrix t ech lyer hs the folloing properties: ii =1 ij =k ji =1/k [ A ] = 11 1 n n n nn = 1 1 n n 1 n n 1 Where n is the number of fctors in prticulr lyer. The reciprocl mtrix t every lyer is used to derive the eight for ech fctor in the hierrchy. The reltionship beteen the eight vector [W] = [ 1,,, n ], nd the reciprocl mtrix [A] is outlined by ( 1.1)

4 1 1 n n 1 n n : 1 1 n = n1 n : n n = n : 1 n (1.1 ) The solution of this system of equtions is knon s the eigenvlue problem. The problem cn hve mny different solutions nd is generlly solved by pproximte numericl techniques. Construction of vlue function to rnk lterntives consists of summing up the eights ssocited ith ech lterntive from the different fctors. The optiml choice is the lterntive tht hs the gretest vlue from the summtion. If the user s judgments re perfectly consistent, elements of the mtrix A conform to (.) referred to s the multiplictive consistency reltion. * = i, j k (.) ij jk ik, In prctice people s judgments re rrely consistent. The AHP model prescribes the use of Consistency Rtio (CR) to mesure the degree of consistency in judgements. A CR of 0.1 or less is considered to be n cceptble level of consistency, CR greter thn 0.1 is considered uncceptble nd the user should revise his/ her judgments to ttin the required level of consistency. Our min concern ith the AHP model is ith the usbility of the model in eb environment. We reduced usbility of the AHP model to to issues: decision mking efficiency (i.e. the time nd effort required to mke decision), nd decision mking effectiveness (i.e. the qulity, ccurcy or comprehensiveness of decision). - A eb user ill not use WDSS if the softre requires (or is perceived to require) too much time nd effort. - A eb user ill not use WDSS if the softre does not provide resonble level of decision qulity for the mount of effort expended. To meet these requirements e designed n optimized AHP model for the eb environment. At conceptul level, the ne eb-bsed IMCF-AHP model differs from the AHP model through the replcement of the concept of Redundncy ith the concept of Interctivity. This conceptul modifiction is believed to deliver more efficient nd effective decision support for eb-bsed systems. The concept of mking redundnt judgments is utilized by the AHP model to improve the ccurcy of user s judgments. Mking redundnt judgments helps verge out errors in judgment. Only (n-1) re essentil (here n refers to the number of fctors in the lyer) to forming reciprocl mtrix [A] since the rest of the entries in the mtrix cn be derived from (.), the AHP model, hoever, prescribes the use of n(n-1)/ judgements (the upper right corner of mtrix A) in order to verge out the errors in

5 judgement. The use of (n-1) insted of n (n-1)/ hs been proposed by mny reserch ppers in order to promote more efficient decision mking (Herrer-Viedm, Herrer et l. 004; Mchris, Springel et l. 004; Wng nd Chen 007). A key difference beteen these models nd the IMCF-AHP model is tht the other models re noninterctive (i.e. ssume the objective of the model is to derive set of eights through single itertion). The IMCF-AHP model implements the concept of interctivity by dividing the processing of informtion into to prts. One prt of the informtion is processed by the humn element, nd the other prt is processed by the computer progrm. Interction is chieved hen the user submits set of preferences. The progrm uses these set of judgments termed User Input Preferences (UIP) to generte Progrm Generted Preferences (PGP), nd combines the to set of preferences to derive ne set of eights. UIP re input by the user nd cn only be chnged by the user, nd PGP re derived by the progrm nd re generlly hidden from the user. This seprtion of preferences llos for more more coopertive humn-computer interction (HCI) system, nd provides for more efficient nd effective decision mking process. After going through severl interctions, the user ill be ble to mke more ccurte nd consistent set of judgments. Other fetures of the model include: the use of fuzzy logic to ccount for uncertinty in users judgments; nd the use of progrmming logic the compenstory strtegy to mke PGP preferences more comptible ith UIP preferences. Fuzzy logic is used to dd more mening to the intermedite vlues described in tble 1. We incorporte incrementl numericl ssignment to implement more grdul trnsition from one verbl description to the next. We define ne vrible the degree of certinty (DOC) in judgment. Numericl ssignments for DOC re described in tble. The vrible ssignments re simply dded to the min numericl ssignments described in tble 1 ithout the mbiguous intermedite vlues hich do not hve precise verbl interprettion. Tble : Guidelines for Degree of Certinty in Judgment User's subjective ssessment of the DEGREE OF CERTAINTY IN JUDGMENT User is certin bout the judgment 0 User is slightly certin the judgment +0.5 User is slightly uncertin bout the judgment +1 User is uncertin bout the judgment +1.5 Numericl Assignment The compenstory strtegy is used to trnslte the numericl scores obtined in the PGP into more comptible verbl scores. PGP vlues re obtined by (.) hich my led to vlues beyond the 1-9 scle, nd vlues tht do not hve precise verbl interprettion. The compenstory strtegy modifies these vlues to mke them comptible ith the verbl scle. In mking this modifiction, the reciprocl mtrix my become inconsistent. The progrm computes the CR nd flgs inconsistent (UIP) judgments hen the CR exceeds the 0.1 threshold.

6 3. The GIMCF-AHP model for group decision mking In situtions here more thn one person needs to prticipte in mking decision s is customry in mny orgniztionl settings, the issue of decision mking effectiveness becomes more slient thn decision mking efficiency. In this context, GDSS is required in order to mnge the group decision mking process (DeSnctis nd Gllupe 1987; DeSnctis nd Gllupe 1993). In this cse, not only is the outcome of the decision importnt, but lso ho the decision s mde (i.e. the decision mking process). The AHP methodology provides extensive support for group decision mking nd llos (the fcilittor, model builder(s) or oner(s) of problem or issue) to construct complex models to ccommodte different group contexts. (Dyer nd Formn 199) describes group contexts s continuum beteen common group contexts, here group members shre the sme bsic objectives, to conflict situtions here prties seek concessions from their opponents. Hierrchicl structuring llos the model builder(s) to dd more lyers to the hierrchy nd to construct decision mking process to fit the most complex decision scenrio. Typicl Hierrchicl structures cn include mny lyers: - Gol, criteri, lterntives - Gol, criteri, sub-criteri, lterntives - Gol, scenrios, criteri, (sub-criteri), lterntives - Gol, ctors, criteri, (sub-criteri), lterntives - Gol sub-criteri, levels of intensities (mny lterntives) A bsic structure includes gol, criteri nd lterntives here: - A Gol is sttement of the overll objective (e.g. select the best lterntive) - A Criterion is fctor tht hs direct bering on the objective. It cn be tngible or n intngible fctor (e.g. cost, qulity, beuty, size, efficiency) - An Alterntive is n object or choice tht is vilble nd helps chieve the ultimte gol. More complex structures cn be chieved by introducing sub-criteri, scenrios, ctors nd levels of intensities here: - A Sub-criterion is decomposition of criterion into sub-fctors (e.g. costs my be decomposed into fixed costs nd vrible costs). - A scenrio cn be used to model uncertinties. A decision outcome my be influenced by the future stte of the economy (e.g. gloom economy, boom economy, nd sttus quo). - Actors or plyers cn be used to model situtions here more thn one person or group needs to prticipte in the decision mking process. The GIMCF-AHP model implements ne concept in hierrchicl structuring. The rounds hierrchy is restructured hierrchy bsed on the use of the IMCF-AHP s the bsic unit of nlysis insted of the level (hich is the bsic unit in the AHP model). A round is defined s set of (n-1) judgments ith prticulr ordering of criteri. The ordering of criteri leds to different set of judgments. Ech ne set of

7 judgments llo us to vie the model from different ngle. For exmple if e re interested in selecting product ith four significnt ttributes: Brnd Nme, Qulity, Price nd Functionlity. We cn utilize four different rounds to derive eights for ech ttribute. Round 1: Brnd Nme in first plce. We compre Brnd Nme Vs Qulity; Brnd Nme Vs Price; Brnd Nme Vs Functionlity. Round : Qulity in first plce. We compre Qulity Vs Brnd Nme; Qulity Vs Price; Qulity Vs Functionlity. Round 3: Price in first plce. We compre Price Vs Brnd Nme; Price Vs Qulity; Price Vs Functionlity. Round 4: Functionlity in first plce. We compre Functionlity Vs Brnd Nme; Functionlity Vs Qulity; Functionlity Vs Price. The eights derived from different rounds llo us to gin more insight into the issues nd provides more flexibility in structuring the decision mking process. A rounds hierrchy cn be expnded to include the full set of rounds to mke comprehensive (unbised judgment) of criteri; or optimized to mke (unbised judgments) through the use of rndom smple of rounds (for lrge number of fctors); or reduced to just one round for non-criticl portions of the hierrchy or in the preliminry phses of model building. 4. Testing the Usbility of the GIMCF-AHP model in decision mking scenrio We describe group decision mking scenrio for bsic hierrchicl structure described in terms of: - A Gol: To Select Weights for portfolio of Stocks - A set of Criteri: Stock Chrcteristics (8 criteri) - Alterntives: Top 10 stocks listed in the Sudi Arbin Stock Mrket The trget Users of the system my include: Investment Clubs, Finncil Services Firms, Mutul Fund Bnk Mngers. To test the system e developed dynmic html Prototype. The min ppliction indo for the prototype is displyed in figures 1 nd.

8 Figure 1: GIMCF-AHP Min Appliction Windo Figure : GIMCF-AHP Min Appliction Windo (bottom hlf)

9 The itertive group decision mking process is initited by lunching IMCF-AHP forms through the buttons mrked Round1, Round, Round3 nd Round4. A representtive form is displyed in figure 3. Figure 3. IMCF-AHP form for Round 1 Input to the form is ccomplished by clicking on the reltive buttons until the user feels confidnt ith his/her selection. Clicking the submit button in the bottom of the form revels the hidden elements of the pge hich include: The Priority Vector, the Sorted Priority Vector nd the Consistency Rtio (figure 4). Figure 4: IMCF-AHP form

10 After revieing the outputs, the user my decide to chnge his inputs, especilly if the consistency rtio exceeds the 0.1 threshold vlue. When the user feels confident ith the judgments, he my click the ExportPriorityVector button to export the sorted priority vector to the min ppliction indo (figure 5). Figure 5: Round1 Sorted Priority Vector exported to min ppliction Windo In the sme mnner Round, Round 3 nd Round 4 re exported. After ll the specified number of rounds, re ccomplished, clicking the Consensus button determines the best ordinl rnking of criteri, the degree of consensus (figure 6) Figure 6: Consensus Rnking of Criteri

11 For Phse II, the process is identicl to phse I, ccept tht ht is exported from the IMCF-AHP eb forms re the eights (figure 7). Figure 7: Phse II & Phse IIb Phse IIb is used to export evlutions insted of eights. This option is utilized if the group ish to ggregte judgements insted of eights or rnkings. The finl phse in the decision mking process is evlution of lterntives ith respect to ech criteri (level ). This is displyed in figure 8. Figure 8: Level Evlution of Alterntives ith respect to ech criteri

12 References Aloysius, J. A., F. D. Dvis, et l. (006). "User cceptnce of multi-criteri decision support systems: The impct of preference elicittion techniques." Europen Journl of Opertionl Reserch 169(1): DeSnctis, G. nd B. Gllupe (1993). Group Decision Support Systems: A Ne Frontier. Decision Support Systems: Putting Theory Into Prctice. R. H. J. Sprgue nd H. J. Wtson. Engleood Cliffs, Ne Jersey, Prentice Hll. DeSnctis, G. nd R. B. Gllupe (1987). "A Foundtion for the Study of Group Decision Support Systems." Mngement Science 33(5): Dyer, R. F. nd E. H. Formn (199). "Group decision support ith the Anlytic Hierrchy Process." Decision Support Systems 8(): Ftny, W. (007). An Interctive, Anlyticl Hierrchy Process (AHP) Progrm for Web-bsed decision support. OR49, Edinburgh, Scotlnd, The OR Society. Herrer-Viedm, E., F. Herrer, et l. (004). "Some issues on consistency of fuzzy preference reltions." Europen Journl of Opertionl Reserch 154(1): Mchris, C., J. Springel, et l. (004). "PROMETHEE nd AHP: The design of opertionl synergies in multicriteri nlysis.: Strengthening PROMETHEE ith ides of AHP." Europen Journl of Opertionl Reserch Mngement of the Future MCDA: Dynmic nd Ethicl Contributions 153(): Sty, R. W. (1987). "The nlytic hierrchy process--ht it is nd ho it is used." Mthemticl Modelling 9(3-5): Sty, T. L. (1977). "A scling method for priorities in hierrchicl structures." Journl of Mthemticl Psychology 15(3): Sty, T. L. (1978). "Modeling unstructured decision problems -- the theory of nlyticl hierrchies." Mthemtics nd Computers in Simultion 0(3): Sty, T. L. (1990). "Eigenvector nd logrithmic lest squres." Europen Journl of Opertionl Reserch 48(1): Sty, T. L. (1990). "Ho to mke decision: The nlytic hierrchy process." Europen Journl of Opertionl Reserch 48(1): 9-6. Sty, T. L. (1994). "Highlights nd criticl points in the theory nd ppliction of the Anlytic Hierrchy Process." Europen Journl of Opertionl Reserch 74(3): Sty, T. L. (003). "Decision-mking ith the AHP: Why is the principl eigenvector necessry." Europen Journl of Opertionl Reserch 145(1): Sty, T. L. nd G. Hu (1998). "Rnking by Eigenvector versus other methods in the Anlytic Hierrchy Process." Applied Mthemtics Letters 11(4): Sty, T. L. nd M. S. Ozdemir (003). "Why the mgic number seven plus or minus to." Mthemticl nd Computer Modelling 38(3-4): Sty, T. L. nd L. G. Vrgs (1984). "Comprison of eigenvlue, logrithmic lest squres nd lest squres methods in estimting rtios." Mthemticl Modelling 5(5): Wng, T.-C. nd Y.-H. Chen (007). "Applying consistent fuzzy preference reltions to prtnership selection." Omeg 35(4):