A NOVEL DECISION APPROACH: INTUITIONISTIC FUZZY IMPORTANCE PERFORMANCE ANALYSIS

Transcription

1 A NOVEL DECISION APPROACH: INTUITIONISTIC FUZZY IMPORTANCE PERFORMANCE ANALYSIS Kuo-Chen Hung Hungkuang Unversty, Tawan Abstract: Importance performance analyss (IPA) s a technque used for conductng a relatve-poston comparson of specfc evaluaton tems by usng mportance (the degree of mportance as perceved by customers) and performance (the degree of customer satsfacton regardng the performance of an enterprse). Moreover, t s an approach for ncorporatng the voce of the customer nto product development and the evaluaton of management performance. Because of numerous factors of uncertanty and lngustc vagueness durng the nformaton collecton process for product desgn, the tradtonal IPA s not approprate for conductng performance analyss. Therefore, ths study proposes a novel ntutonstc fuzzy sets (IFSs) IPA performance evaluaton model. In addton, analytcal network processng was combned wth the model and benchmarkng enterprse compettveness was consdered. Ths model can solve the ambguty and decson-makng problems that currently exst n questonnares. Thus, t drects the focus on the objectve features emphaszed by customers, and provdes enterprses wth a practcal evaluaton model for relatve product desgn or decson evaluaton. Keywords: ntutonstc fuzzy sets, mportance performance analyss, analytcal network process, decson analyss 52

2 . INTRODUCTION The IPA s an analytc tool used for analyzng consumers emphass on qualty attrbutes and ther evaluaton of enterprse performance level; subsequently, t can also be used to prortze the mportance degree of attrbutes and ts correlaton wth performance levels (Sampson and Showalter (), Hansen and Bush (), Chu and Cho (2000)). The analyss results can be provded to enterprses for the evaluaton of attrbute performance, and can be used as a reference for the future operaton and development of an enterprse and the mprovement of the current status of customer relatons. The IPA was frst proposed by Martlla and James (), who used the IPA to analyze product attrbutes n the automoble ndustry. The prmary concept was to compute the mean values of the mportance degree and performance level n a two-dmensonal matrx, whch was adopted to dentfy the relatve postons of attrbutes possessng varous mean values. Martlla and James () subsequently suggested practcal recommendatons and strategc applcatons for specfc qualty attrbutes. However, Hollenhorst et al. (2) observed that the analyss results produced by Martlla and James (), who used the medan of the two-dmensonal matrx to evaluate enterprse servce attrbutes, dd not correspond to the actual stuaton. Thus, Hollenhorst et al. (2) proposed usng the overall means of the mportance degree and performance level as the dvdng ponts for the axes of the IPA two-dmensonal matrx. Therefore, the dstrbuton of the qualty attrbutes n the matrx featured hgh determnaton ablty. For enterprse managers, analyzng market competton s necessary for enterprses to obtan compettve advantage. By adoptng customer evaluaton scores of enterprse performance levels as the bass for the comparson between the case enterprse and the optmal compettor, and by employng the performance rato (PR) analyss method, an understandng of the gap between the market compettveness of two enterprses and ther postons n the market can be acheved. Ths study proposes a modfed IPA model, whch was ncorporated wth the concept of enterprse benchmarkng and combned wth the PR concept proposed by Garver (2003). Furthermore, the analyss method of PR was adopted to calculate the market compettveness gap between two enterprses, and the calculaton results were used to replace the y-axs n the tradtonal IPA dagram (satsfacton degree). The standardzed measurement was expected not only to effectvely avod the drawbacks of tradtonal IPA assumptons, but also to be used n the quanttatve compettveness analyss of the case enterprse and ts outstandng compettors. The meanngs of the four IPA quadrants are as follows (Martlla and James (), Zhang and Chow (2004)): (a) Quadrant I (Keep Up the Good Work): Ths area s emphaszed by the customers and currently perceved by the consumers as exhbtng a satsfactory performance level; thus, t s the prmary source of enterprse compettve advantage, whch enterprses should endeavor to mantan. (b) Quadrant II (Possble Overkll): Ths area exhbts a superor performance level, whch s not focused on by the customers but s currently perceved by the consumers. Ths s the second source of enterprse advantage; the enterprse should not overly nvest resources n ths area. (c) Quadrant III (Low Prorty): Ths area s not emphaszed by customers and perceved by consumers as featurng a low performance level. Ths s the second source of enterprse dsadvantage, whch must be mproved after Quadrant IV has been mproved. (4) Quadrant IV (Concentrate Here): Customers pay attenton to ths area, but the performance perceved by consumers does not acheve the expected level. Attrbutes located n Quadrant IV are the key factors determnng the future development of enterprses. Therefore, an enterprse must nvest more resources to mprove ths area, whch s the prmary source of enterprse dsadvantage, also called Crtcal Qualty Attrbutes. To fulfll an optmal alternatve, reachng a consensus through expert group decson-makng s vtal. In ths study, one of the ams was to understand the problem of expressng uncertantes, namely, agree, dsagree, and neutral, durng the decson-makng process. Although Deng (2008) and Wang and Tseng (20) have proposed applyng the ntegraton of fuzzy theory and IPA to the performance evaluaton of varous servce attrbutes. However, compared wth fuzzy theory, IFSs theory exhbts a superor capacty for conformng to the logcal thnkng of people n the form of lngustc expresson. Scholars have not appled IFSs to IPA. Therefore, ths study constructed an IFSs-IPA model that was appled to the desgn of green products. 522

3 2. BACKGROUND THEORIES 2. Intutonstc fuzzy sets (IFSs) Zadeh (65) proposed fuzzy theory as a soluton for the subjectve conscousness and uncertanty that exst n the thnkng modes of people. Fuzzy sets were adopted to descrbe objects, and fuzzy lngustc varables were quantfed nto values through the membershp functon to denote the degree of membershp between agree and dsagree. However, the neutral state was excluded. Thus, the IFSs theory proposed Atanassov (86) developed a method for solvng the problem of neutralty. The values used for representng the degree of membershp n the tradtonal fuzzy theory was changed to ratos, whch can express not only agree and dsagree but also neutral. In other words, the lngustc expresson derved from the IFSs can accord wth the logcal thnkng of people. Accordng to Atanassov (86) and Gau and Buehrer (3), the defnton of IFSs s as follows: A = x, μ x, v x x X, { } Defnton : Let X be a unverse, then the IFSs A n X s presented as ( ) ( ) A A where μ ( x) : X [ 0, A ] denotes the membershp of agree, and ( ): [ 0, A ] membershp of dsagree. Because μ ( x) + v ( x), μ A A ( x A ) va( x) neutral. For example, f A { x,0.6,0.3 x X} v x X denotes the sgnfes the membershp of = s explaned usng electon poll ratngs, then 60% of the people support somethng, 30% of the people oppose somethng, and 0% of the people are neutral. A x, μ x, v x x X B = x, μ x, v x x X are IFSs n X. The { } A A { } B B Defnton 2: = ( ) ( ) and ( ) ( ) addton and multplcaton formulas for sets A and B are as follows: A + B = x, μ x + μ x μ x μ x, v x v x () { ( A( ) B ( ) A( ) B ( ) A( ) B( ))},( μ ( ) μ ( ), A B A( ) B ( ) A( ) B( )) { } A B = x x x v x + v x v x v x (2) 2.2 Analytcal network process (ANP) The ANP was proposed by Saaty (6) to solve the problem of possble nterdependence among aspects or crtera and the feedback effect, whch exsts n the framework of the tradtonal analytc herarchy process (AHP). In the tradtonal analyss of AHP, a herarchy attrbute s assumed to be mutually ndependent of other herarchy attrbutes and possble alternatves. Thus, the decson-makng problems only feature herarchcal relatonshps. However, n an actual decson-makng envronment, numerous decson problems cannot be constructed based smply on herarchcal relatonshps, because the problems may nvolve the nteracton relatonshps among the AS n the same herarchy or the effect of nterdependence among varous herarches. Moreover, Meade and Presley (2002) and Saaty (2006) contended that the subordnate relatonshps between herarches are dffcult to clearly dentfy n some problem structures. A herarchy may smultaneously domnate and be domnated by other herarches, whch s the feedback effect problem. In other words, herarchcal structures that feature a top-down lnear pattern cannot effectvely solve complex decson problems. The development of ANPs nvolved the adopton of the network process concept to mprove the lmtaton of ndependence derved from the herarchcal structure. To solve the nterdependency relatonshps among the elements n a problem structure, a supermatrx was adopted n the ANP method to calculate the relatve weght of each element. The supermatrx comprses numerous submatrces, n whch a blank space or 0 denotes the ndependence among the groups or crtera. A major advantage of ANP s that t can be used to evaluate the nner and outer nterdependence of crtera. Outer nterdependence refers to the relatonshps n whch the groups are mutually nfluenced, and nner nterdependence refers to the nterdependency relatonshps between each crtera n the same group. A supermatrx conssts of several submatrces, whch comprse egenvectors produced by the mutual comparson between each crtera. The varable M' denotes the unweghted elementary matrx. The column values may not correspond to the column-stochastc prncple (for example, the sum of column values s not equal to ) and thus need to be converted usng a specfc procedure to obtan the weghted supermatrx M. Through the converson procedure and the process of lmtng, M and M' were multpled to the power of 2k+ (k was decded subjectvely); subsequently, a converged lmt value was obtaned. The lmt value was fxed and was the relatve weght among the elements (Saaty, 6). 523

4 We (2008) combned fuzzy Delph wth ANP and appled them to the green desgn of products to ensure that the development of new products enabled the contnuous growth of company operaton. Furthermore, Lu and Ln (200) contended that establshng an optmal evaluaton alternatve for envronmental strategc orentatons for green nnovaton s a crucal step for enterprses development of green nnovaton n the current stage. Thus, Lu and Ln ntegrated the decson makng tral and evaluaton laboratory (DEMATEL) method wth ANP to obtan crucal nfluencng factors and weghts for the green envronmental strategc orentatons, whch enterprses can reference when developng green nnovaton strateges. 3. RESEARCH METHOD In ths study, an IFSs-IPA model was constructed consderng complex human thnkng and behavor modes and the ambguty of people s preferences. The evaluaton scores provded by experts for each aspects (AS) and crtera (C) were converted to the ntutonstc fuzzy nterval values; the score standard was based on the ntutonstc fuzzy lngustc converson scale developed by L (20); n the scale, μ denotes agree, and v denotes dsagree. (Atanassov, 86) The ntutonstc fuzzy lngustc scale s dsplayed n Table. Table : The ntutonstc fuzzy lngustc converson scale Lngustc Very mportant Important Neutral varables Slghtly mportant Not mportant at all IFS( μ, ν ) (0.5, 0.05) (0.0, 0.25) (0.50, 0.40) (0.25, 0.0) (0.05, 0.5) In ths study, the modfed IPA evaluaton model was adopted. Based on the concept of IFSs, the overall means of the mportance degree and performance level were used as the dvdng ponts to dvde the two-dmensonal matrx nto four quadrants. In addton, the voces of the customers and experts were collected based on the concept of IFSs; the ANP expert questonnare was produced by usng IFSs as proposed by Atanassov (86). The experts n the decson-makng group were asked to determne the relatve mportance degrees among C. Subsequently, the relatve weghts for the customer requrements for products were calculated and dsplayed on the x-axs. The customer-provded evaluaton scores for the enterprse performance level were adopted as the baselne for the case enterprse to compare wth the optmal compettor; the market compettveness gap between the two enterprses was calculated usng PR and subsequently dsplayed on the y-axs. The four quadrants were employed as the analyss tool for measurng the customer-perceved mportance and satsfacton degree regardng the qualty attrbutes of green product nnovaton. The four quadrants can also be referenced by enterprses to mprove servce qualty and decde marketng strateges. The operaton procedure used n ths study s as follows: Step : Step 2: The development of AS for the goal herarchy n green product nnovaton. The decson goal was frst confrmed. Relevant nformaton regardng green nnovaton was collected by conductng a lterature revew and gatherng expert opnons. The evaluaton aspect ( AS ) and crtera ( C ) were extracted, where =,,m and j =,,n. The performance degree (S) and PR exhbted by the case enterprse and the compettor n the development of AS and C for green product nnovaton were computed as the y-axs n the modfed IPA matrx. Based on the ntutonstc fuzzy lngustc scale n Table, the expert group provded performance scores for the AS and C of green product nnovaton developed by the case enterprse and the compettor. Referencng the approach adopted by Klr and Yuan (5), the geometrc mean was used to converge the ntutonstc fuzzy scores provded by the expert group nto a sngle ntutonstc fuzzy score, as dsplayed n Equatons (3) and (4). Furthermore, the ntutonstc fuzzy set scores derved from the expert group were converged, the results of whch were then defuzzfed usng the approach adopted by Hung et al. (2008), as shown n Equaton (5). Thus, the crsp performance values (S) between each AS and C for the products developed by the case enterprse and the compettor were obtaned. S % ( μ) = k ( S ( μ)... S k ( μ) ); =,..., m; j =,..., n; k =,..., c (3) 524

5 Step 3: k k Sv %( ) = ( S( v)... S( v) ); =,..., mj ; =,..., nk ; =,..., c (4) ( x) S = μ ;,, m; j,..., n μ ( x) ν ( x) = K + = (5) Ths study adopted the modfed IPA model. The customer-provded evaluaton scores for the enterprse performance level were adopted as the baselne to compare the case enterprse wth the optmal compettor and dentfy the poston of the enterprse n the market. Addtonally, the concept of PR can facltate the understandng of the market compettveness gap between the two enterprses. Therefore, the PR of the average satsfacton value of every servce tem of the case enterprse to that of the compettor s was calculated by usng Equaton (6). The tradtonal IPA performance value was replaced by the PR value (Y-axs). PR = θ (6) ρ Where θ denotes the average satsfacton value of the servce qualty provded by the case enterprse. The ρ denotes the average satsfacton value of the servce qualty provded by the compettor. The mportance degree (I) of the AS and C for green product nnovaton was computed as the x-axs n the IPA matrx. Step 3.: Based on the ntutonstc fuzzy lngustc scale n Table, the expert group provded mportance degree (I) scores for the AS and C of green product nnovaton. The obtaned scores were defuzzfed usng the approach provded by Hung et al. (2008), as shown n Equaton (5). Subsequently, the crsp values of the relatve weghts (I ) for each AS and C were obtaned and normalzed usng Equaton () to be the weghts ( I ). = j= normal I normal I = ; =, K, m; j =, K, n () m n I Step 3.2: The normalzed weghts of the AS and C for the submatrces, whch were obtaned n Step 3., were ntegrated to obtan the unweghted supermatrx M'. Because the column values n the unweghted supermatrx may not correspond to the column-stochastc prncple, M was converted to be a weghted supermatrx M. M was then multpled to the power of k usng Equaton (8) to yeld a lmtng supermatrx M*, through whch the mportance degree I for the AS and C of green product nnovaton were obtaned. * M = lm M k ; k power (8) k Subsequently, a parwse comparson between the matrces for AS and was conducted followed by consstency testng. Accordng to Saaty (80), for matrces of the same herarchy, the consstency rato (CR) s requred for consstency testng, whch s the rato of the consstency ndex (CI) to the random ndex (RI), as shown n Equatons () and (0). The degree of consstency for matrces s acheved when the CR value s smaller than 0.. CI = ( λmax n) ( n ) () CR = CI RI (0) where λ denotes the maxmum egenvalue, and n denotes the number of max herarches for the gven matrx. Step 4: The PR values acqured n Step 2 for the AS and C of green product nnovaton were adopted as the vertcal axs (the y-axs) n the IFSs-IPA model. The values of mportance degree (I) acqured n Step 3 for the AS and C of green product nnovaton were adopted as the horzontal axs (the x-axs) n the IFSs-IPA model. The evaluaton results of AS and C were ncorporated n the IFSs-IPA performance evaluaton matrx. Therefore, The IFSs-PA performance evaluaton matrx has been produced. C 525

6 Step 5: The IFSs-IPA performance evaluaton matrx obtaned n Step 4 for the development of green product nnovaton was used n analyses on strengths and weaknesses and evaluaton of management mplcaton regardng the strateges of green product nnovaton. Thus, enterprses can use t as a reference for effectve operatons. Thus analyses on strengths and weaknesses were conducted. 4. CASE VERIFICATION Due the surgng popularty of envronmental conscousness and the concept of a sustanable earth, green product nnovaton has become an essental topc for modern enterprse operaton and management. In response to the need of technque development regardng the modularzaton of new-generaton fuel cells, the case enterprse mplemented green product development and nnovaton to fulfll the envronmental protecton requrements of customers. Thus, ths study adopted a Tawanese fuel cell-producng enterprse as the case study example. Ths enterprse was analyzed by followng the fve steps stated n Secton 3 shown as the followng, Step : Four aspects and twelve crtera regardng green nnovaton requrements were proposed to evaluate the nnovatve desgn requrements for the new-generaton fuel cell module, as shown n Table 2. The crtera were obtaned by ntervewng experts. Moreover and the ANP was adopted to construct an evaluaton model to nvestgate the nterdependency relatonshps between the crtera and the alternatves as well as the nterdependency relatonshps among the crtera. The results can be provded as a reference for enterprses n the development of green products. Fgure dsplays the nterdependency and feedback relatonshps among the aspects and crtera. Table 2: The AS of the requrement herarchy n green product nnovaton Aspect (AS) Crteron (C) Energy savng (AS) Producton lne automaton (C) Full prntng (C2) Hgh transfer effcency (C3) Amount reducton (AS2) Lead-free nk (C2) Ink dluton (C22) Slver wre thnnng (C23) Recyclng (AS3) Hgh productve capacty (C3) Slcon substrate thnnng (C32) Wafer sze enlargement (C33) Easy processng (AS4) Prntng fxtures (C4) Vsual postonng (C42) Double table (C43) Fgure : Network herarchy dagram for the goal of green product nnovaton Step 2: Targetng the performance degrees of the goals, AS, and C of green product nnovaton mplemented by the case enterprse and the compettor, the expert group conducted an ntutonstc fuzzy lngustc evaluaton. Usng Equatons (3) and (4), the collected expert-group IFSs scores were converged, the results of whch were used n Equaton (5) to obtan the crsp performance values. Then usng the Equaton (6) computes the PR values shown n Table

7 Table 3: PR values for the mplementaton of green product nnovaton AS obtaned by the case enterprse and the benchmarkng compettor PR values for the mplementaton of green product nnovaton AS Items Goal AS AS2 AS3 AS4 C C2 C3 C2 C22 C23 C3 C32 C33 C4 C42 C43 s Case enterprse compettor PR values Step 3: Based on the ntutonstc fuzzy lngustc scale n Table, the expert group provded ntutonstc fuzzy scores for the mportance degrees of the green product nnovaton aspects and crtera. Furthermore, the expert-group IFSs scores were converged, and the results were used n Equatons (3) and (4) to acqure the crsp values of relatve weghts. The relatve postons of the submatrces n relaton to the supermatrx were establshed. Usng the weghted supermatrx M was lmted to obtan the lmtng supermatrx M*. Thus, mportance degree (I) weghts of the aspects and crtera of green product development were acheved, as shown n Table 4. Table 4: Lmtng supermatrx M* Step 4: The performance and mportance degrees obtaned n Steps 2 and 3 were collated n Table 5. The data were then ncorporated n the IFSs-IPA evaluaton matrx proposed n ths study to analyze the competton strateges for green ndustry nnovaton. Table 5: The case enterprse s current mplementaton status regardng green product nnovaton The mplementaton of each AS for green product nnovaton Importan ce degree PR Goal s AS AS2 AS3 AS4 C C2 C3 C2 C22 C23 C3 C32 C33 C4 C42 C43 Overal l mean Fgure 2: IFSs-IPA analyss dagram derved from case verfcaton. 52

8 Step 5: Based on Table 5, the IFSs-IPA performance evaluaton matrx (Fgure 2) was establshed for the aspects and crtera of green product nnovaton, and analyses of strengths and weaknesses were subsequently conducted. Ths study ntegrated the concept of IFSs wth IPA, and appled the IFSs-IPA model to the product desgn and development of the modularzaton process of green fuel cells. Based on the concepts of agree, dsagree, and neutral, the performance scores were converted to ntutonstc fuzzy lngustc values. Thus, the case study verfed that the IFSs-IPA model exhbted a superor performance capacty for processng uncertan nformaton and solvng multattrbute decson-makng problems. Addtonally, the customer requrements and the AS mportance degree scores can be acqured usng objectve thnkng. 5. DISCUSSION AND ANALYSIS The Fgure 2 dsplays the data of AS and C requred n green nnovaton dstrbuted n the four quadrants of the matrx, representng four types of resource dstrbuton exhbted by the enterprse. The meanngs of the quadrants were as follows:. The research results show that the evaluaton tems located n Quadrant I (Keep Up the Good Work) were the foundatons for the enterprse to develop green product nnovaton. The tems nvolved green ndustry nnovaton (Goals), energy-savng (AS), amount reducton (AS2), and easy processng (AS4), suggestng that the effort made by the case enterprse on these tems n green product nnovaton was consstent wth the expectatons of the customers. Moreover, the customer satsfacton degree acqured by the case enterprse was hgher than that acqured by the major compettor. Thus, the enterprse compettve advantage les n Quadrant I. The key factors for the enterprse to mantan ts compettveness n the ndustry and ts sustanable development are mantanng ts servce standards and constantly sparng no efforts to nnovate and develop green products. 2. The evaluaton tems located n Quadrant II (Possble Overkll) comprsed full prntng (C2), hgh transfer effcency (C3), nk dluton (C22), slver wre thnnng (C23), slcon substrate thnnng (C32), wafer sze enlargement (C33), prntng fxtures (C4), and vsual postonng (C42). The majorty of tems were located n Quadrant II, suggestng that although the tems provded by the enterprse were superor to those provded by the compettor, the enterprse possesses consderable experence n the photoelectrcty and solar energy ndustres and thus has nvested too much resources n these tems. Thus, the customer satsfacton degree regardng the servce qualty pertanng to green product nnovaton by far exceeded ther expectatons of the enterprse performance degree. Thus, the enterprse should rearrange the overall resource dstrbuton and nvest resources n tems located n Quadrant IV, whch feature hgh mportance degrees but low satsfacton. 3. The tems located n Quadrant III (Low Prorty) nvolved producton lne automaton (C), lead-free nk (C2), hgh productve capacty (C3), and double table (C43). Compared wth the other servce attrbutes of green ndustry nnovaton, the customers perceved the mportance degrees of these tems as low. Addtonally, the performance degrees of these the provded by the enterprse were nferor to those provded by the compettors. Consequently, the enterprse should ntegrate and employ more resources (such as resources from the government, research nsttutons, and schools) n ths area to surpass ts compettors. Thereby, the customer satsfacton degree can be mproved, and the enterprse s compettve advantage n green product nnovaton can be enhanced. 4. Only one tem was located n Quadrant IV (Concentrate Here), whch was recyclng (AS3). Ths suggests that customers perceved ths tem as hghly mportant, and that the satsfacton degree regardng the enterprse mplementaton was lower than that of ts major compettor. In other words, the enterprse has not completely mplemented ths servce tem. The concept of recyclng should be enhanced regardng the effectve recyclng desgned for components related to machnery facltes. Falng to mplement ths tem may not only nfluence the enterprse performance regardng the green product manufacturng process, but also cause the product desgn of ths enterprse to fall far behnd that of ts compettors. 6. CONCLUSIONS For the evaluaton model constructed by ths study, the ntutonstc fuzzy mportance degree data were combned wth the ANP to calculate the mportance degree weghts for the evaluaton tems, 528

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