The Application of Uninorms in Importance-Performance Analysis

Transcription

1 The Applcaton of Unnorms n Importance-Performance Analyss BENOIT DEPAIRE, KOEN VANHOOF, GEERT WETS Department of Busness Studes Hasselt Unversty Campus Depenbeek, Agoralaan Gebouw D, 3590 Depenbeek BELGIUM benot.depare@uhasselt.be Abstract: In the feld of marketng, Importance-Performance Analyss s a useful technque for evaluatng the elements of a marketng program. The mportance dmenson of ths technque s often determned n a regresson based approach. However, ths approach has certan problems and lmtatons. A new approach, based on unnorms, s suggested. Ths artcle shows that the unnorm approach possesses several strengths for ths type of analyss and matches partcularly well wth the customer satsfacton theory. Key-Words: Fuzzy Set Operators, Unnorms, Renforcement Behavor, Compensaton Behavor, Importance- Performance Analyss, Expectaton-Dsconfrmaton Paradgm 1 Introducton In the feld of marketng, Importance-Performance Analyss (IPA) s a useful technque for evaluatng the elements of a marketng program. Its ease of nterpretaton makes t an attractve manageral tool for developng marketng strateges [6]. Due to ts strength and manageral attractveness, IPA s also used as part of operatons strategy formulaton [12], as analyss tool n customer satsfacton management [7, 8] and n servce qualty mprovement programs [11]. The IPA technque calculates the mportance and performance of each product/servce attrbute. Next, these couples of data are plotted on a grd wth performance and mportance as the two dmensons. The axes dvde the grd nto four dfferent quadrants, each wth ther own specfc nterpretaton: concentrate here, keep up the good work, low prorty and possble overkll. Each attrbute les n one of these four quadrants, allowng the manager to easly dentfy the attrbutes that requre the most urgent attenton. Generally, the attrbute performance s drectly measured, by use of a survey. The calculated mean (or medan) of all observed attrbute performances are used as the performance dmenson coordnate n the IPA grd. Ths s the standard approach. Wth regard to the mportance dmenson of each attrbute, two types of approaches exst,.e. the drectly measured approaches [6, 11, 12] and the ndrectly measured approaches [7, 8]. However, recent research results n the feld of customer satsfacton queston the usablty of one of the most common ndrectly measurement approaches of attrbute mportance,.e. regresson coeffcents. In the next secton, the problems of the most common regresson based approach are emprcally demonstrated. Next, a unnorm approach wll be suggested. Fnally, a case study llustrates the potental of ths approach n the feld of IPA research. 2 Regresson based mportance measures The regresson based approach, commonly appled n IPA and customer satsfacton research, regresses the overall satsfacton on the attrbutes performances. The mpact of these attrbutes performances on the overall satsfacton, measured by the regresson coeffcents, can be used as proxes for the attrbutes mportance measures [2, 8, 9]. Because ths approach tres to ft the data to an a pror defned model, t s mportant to make the correct assumptons about the data and the regresson model. Generally, the followng regresson model s used, where Y represents the customer satsfacton and represents the performance of attrbute. Y = α 0 + β u (1) + However, ths regresson model assumes that the mpact of the attrbute performance on the overall satsfacton can be represented as a pont-estmate, whch s n contradcton wth results of recent research [8, 9, 11]. Recent research ponted out that the attrbute mportance s dependent on the attrbute performance. Accordng to Sampson et al. [11], ths mples that the regresson coeffcent, whch s a pont-estmate, only captures a fracton of the true mpact. The part that s not captured by the regresson coeffcent hdes nsde the error term, makng t heteroscedastc and volatng one of the assumptons of ordnary least squares (OLS) regresson.

2 Furthermore, Equaton 1 also assumes that no nteracton effects exst between the attrbute performance varables exst. Ths mples that s mpact on overall satsfacton wll not alter f attrbute j s performance drops from e.g. 9 out of 10 to 2 out of 10, gven the same performance for and ceters parbus. However, ths seems to be a rather unexpected type of behavor. Therefore, both the (heteroscedastc) nature of the dsturbance term and the necessty of nteracton terms are emprcally tested. 2.1 Data Ths research ncludes data from a customer satsfacton survey wthn the famly entertanment sector. The survey measures 7 attrbute performances and 1 overall satsfacton score for each customer. All performance/satsfacton scores were measured on a scale from 1 (extremely low) to 10 (extremely hgh). In total, ths customer satsfacton survey was repeated for 7 companes n the entertanment sector. The number of observatons s reasonably hgh,.e. mnmum 500 cases per company. 2.2 Heteroscedastcty Heteroscedastcty means that the varance of the dsturbance term s related to the values of the ndependent or dependent varables. To verfy the presence of heteroscedastcty n the dsturbance term, 7 regressons were performed, one for each company. Each regresson follows the model formulated n Equaton 1. The regresson results show that 77% of all regresson coeffcents are statstcally sgnfcant at the level of 1% and 87.5% of all regresson coeffcents are statstcally sgnfcant at the level of 5%. The adjusted R² les between 52% and 74%. At frst sght, these regresson results seem to be reasonably good. However, these results gve no ndcaton about the nature of the dsturbance term. To nvestgate whether heteroscedastcty s n play or not, further tests are necessary. In ths research, two heteroscedastcty tests were appled to the data. The frst test s based on the graphcal analyss of the dsturbance term, whch s an nformal method. Ths method plots the squared resduals û, whch are a proxy for the varance of the dsturbance term [5], aganst. Any patterns revealed by these plots ndcate a relatonshp between the squared resduals and the ndependent varables, mplyng the presence of heteroscedastcty. To measure the strength of the pattern, correlaton coeffcents were determned between û and the ndependent varables. The results are shown n Table 1. Statstcally sgnfcant correlaton coeffcents are consdered to ndcate heteroscedastcty. Frst of all, the results of Table 1 show that all seven regressons have a dsturbance term whch s heteroscedastc, related to at least one ndependent varable. Secondly, 87.5% of all statstcal sgnfcant correlaton coeffcents have a negatve sgn. These results show that the presence of heteroscedastcty s most lkely. However, t s stll possble that the magntude of the problem s underestmated, because the correlaton coeffcents only test for lnear relatonshps. Table 1 Correlaton coeffcents Attrbute Spearman rank s correlaton coeffcent Company * * * -0.23* * * * -0.13* * * * * -0.31* * sgnfcant at 1% sgnfcant at 5% sgnfcant at 10% Therefore, the more formal Goldfeld-Quandt heteroscedastcty test was appled. Ths popular method s applcable f one assumes that the heteroscedastc varance, σ 2, s postvely related to one of the explanatory varables n the regresson model [5]. However, the correlaton coeffcents from the prevous test ndcated a negatve relatonshp n most of the cases. Therefore, we adapted the Goldfeld-Quandt approach to test for both type of relatonshps. Tradtonally, the G-Q test starts by rankng the observatons n ncreasng order, accordng to the values of. Secondly, the data s splt n two sets, omttng the mddle n observatons. Next, an OLS regresson s ftted to both data set 1 (smallest values) and data set 2 (largest values). If no heteroscedastcty s present, the RSS of both regressons should not dffer sgnfcantly and Equaton 2 should follow the F dstrbuton. To adjust ths approach, n order to test for a negatve relatonshp, t suffces to rank the observatons n decreasng order or to calculate λ dfferently, by swtchng nomnator and denomnator n the orgnal formula. RSS1 / df λ = (2) RSS2 / df Table 2 shows the heteroscedastcty results for both the correlaton coeffcents test and the Goldfeld-Quandt test. The G-Q test detects clearly more heteroscedastcty than the correlaton coeffcents test. However, for all cases except one, when both tests agree on heteroscedastcty, they ndcate the same type of relaton between the varance of the dsturbance term and the ndependent varable. Ths valdates the fact that both negatve and postve relatonshps exst. Fnally, n

3 contrast wth the results from the correlaton coeffcents test, the G-Q test reveals that the varance of u s not more lkely to be negatvely than postvely related to. However, we can conclude that heteroscedastcty s present. Table 2 Heteroscedastcty results Company Attrbute CC GQ CC GQ CC GQ CC GQ CC GQ CC GQ CC GQ 1 P* P P* N N* N N N* N* 2 P P* N N* N* N* N* N* 3 P* N P* P P P* N N* N* N* 4 P* N P* P P P N N* 5 N N* N N* N* N N* N* N N* N* N* 6 P* P* N* P N N* N 7 P* P N P N* N N* N CC Correlaton coeffcent test GQ Goldfeld-Quandt test P Varance of u s postve related to N Varance of u s negatve related to * sgnfcant at 1% sgnfcant at 5% sgnfcant at 10% The varance of u, homoscedastc or heteroscedastc, plays no part n the determnaton of the unbasedness property [5]. Ths mples that the OLS estmated regresson coeffcents are stll unbased and lnear. However, they no longer have the mnmum varance n the class of lnear unbased estmators. Therefore, the varance of the regresson coeffcents are overestmated or underestmated on the average, and n general, t s mpossble to know f the bas s postve or negatve. As a consequence, the conventonally computed confdence ntervals and t and F tests are no longer relable. 2.3 Interacton effects In Importance-Performance Analyss and other customer satsfacton research, the regresson model often mplctly assumes no nteracton effects exst among the attrbutes performances. The purpose of ths study s to test the valdty of ths no nteracton assumpton. Ths study only consders two-factor nteracton effects. The effect of s assumed to ncrease as the performance of j decreases and vce versa. Therefore, nteracton effects of the type / j are added to the regresson model. Equaton 3 shows the new regresson model, after addton of the nteracton effects. Many other and more complex nteracton effects can be ncorporated nto the model. However, t s not our goal to dentfy all possble nteracton effects, but merely to test the no nteracton assumpton. j Y = α 0 + β + γ j + u (3) j j In total 14 regressons were performed,.e. both the regresson wth and wthout the nteracton effects for each company. However, because of the hgh amount of nteracton effects, a stepwse varable selecton approach was used to add the 42 nteracton effects to the model. Ths approach adds the nteracton effect whch has the smallest probablty of F, f that probablty s equal to or less than Interacton effects already n the regresson equaton are removed f ther probablty of F becomes equal to or larger than The method termnates when no more varables are elgble for ncluson or removal. Table 3 shows the results of the regresson for the frst company. After completng the stepwse regresson, 8 nteracton effects were added to the orgnal model, each of them beng statstcally sgnfcant. Furthermore, the adjusted R² ncreases from 51.9% to 58.2%, whch ndcates that the model wth nteracton effects s able to explan more varaton n the dependent varable. Furthermore, Table 3 also shows that the regresson coeffcents dffer sgnfcantly when nteracton effects are added to the regresson model. Some of the man effects even get a negatve coeffcent. However, the nterpretaton of these negatve coeffcents has become less trval wth the nteracton effects n play. Table 3 Regresson wth(out) nteracton effects Independent varables Model A Model B Man effects Interacton effects Intercept 1.58* -5.99* * * -0.28** ** -0.72* ** -0.86* * -0.64* * -0.43* 6 / * 4 / * 1 / * 4 / * 6 / * 4 / * 3 / * 3 / ** Adjusted R² Model A no two-factor nteracton effects Model B wth two-factor nteracton effects * sgnfcant at 1% ** sgnfcant at 5% Table 4 Regressons wth nteracton effects - summarzed results Company Δ Adjusted R² # Interacton effects* * sgnfcant at 1% Fnally, Table 4 summarzes the results for all seven regressons (wth nteracton effects). These results

4 strongly ndcate that nteracton effects are present n the customer satsfacton process. As a consequence, a specfcaton error s made when one leaves the nteracton effects out of the regresson. The consequences of omttng a relevant varable depend on the correlaton between the omtted varable and the ncluded varables. If they are correlated, the regresson coeffcents of the ncluded varables are based. But even n case of no correlaton, although the regresson coeffcents of the ncluded varables are unbased, ther varances are based, makng the t and F tests unrelable. 2.4 Concluson The results of our research offer emprcal evdence that the smple regresson model used n IPA and customer satsfacton research (Equaton 1) suffers from both heteroscedastcty and model-specfcaton problems. Both problems have ther consequences. Heteroscedastcty, f not accounted for, leads towards unrelable confdence ntervals and unrelable t and F tests. Ths makes t very dangerous to order the attrbutes accordng to ther mportance (.e. ther regresson coeffcent). Omttng the nteracton effects leads toward unrelable confdence ntervals at best and based regresson coeffcents at worst. Our emprcal results show ndeed that the regresson coeffcents of the smple model dffer greatly from the regresson coeffcents of the model wth nteracton effects, the latter havng more explanatory power. Based on these fndngs, we jon Sampson et al. n ther concluson that the smple regresson model, often used n IPA, s problematc and unrelable. Further research s needed to adjust the regresson model n order to avod both heteroscedastcty and specfcaton errors. However, we beleve that a new approach, whch wll be presented n the next secton, based on unnorms, can be an nterestng alternatve to calculate attrbute mportance 3 Unnorm based mportance measures 3.1 Unnorms n customer satsfacton theory Importance-Performance Analyss s closely related to customer satsfacton concepts. The mportance of an attrbute s often nterpreted as the mpact of the attrbute on the customer satsfacton (e.g. [7], [8]). Furthermore, customer satsfacton theory s an mportant topc n marketng research and t s wdely accepted that customers generate a mult-attrbute-based response on ther satsfacton wth a certan product/servce. In a certan way, customer satsfacton can be consdered as the aggregaton of the customer s attrbute-level experences [15]. Ths process of nformaton fuson has been thoroughly studed n past research. The last 10 years, an mpressve organzed collecton of aggregatve operatons has been developed wthn the feld of fuzzy set theory and non-classcal decson theory [4]. Ths collecton can be dvded nto several famles of aggregaton operators, each of them havng specfc mathematcal and behavoral propertes [1]. Ths research uses the unnorm aggregator famly to model the customer satsfacton process. A unnorm U s a mappng U: [0,1]x[0,1] [0,1] havng the followng propertes [16]: 1. U(a,b) = U(b,a) 2. U(a,b) U(c,d) f a c and b d 3. U(a,U(b,c)) = U(U(a,b),c) 4. There exsts some elements e [0,1] called the dentty element such that a [0,1]: U(a,e) = a The above defnton shows the mathematcal propertes of the unnorm operators. We wll concentrate on the fourth property, whch plays an mportant role n our research. For a full dscusson of the mathematcal propertes of the unnorms, the reader s referred to [1, 15, 16]. The fourth property defnes the neutral element of a unnorm, whch plays the role of a null vote n the aggregaton process and dstngushes the unnorm from the t-norm and the t-conorm. The neutral element s mportant because t defnes the behavor of the aggregaton operator. If the arguments of the aggregaton operator are both smaller (larger) than the neutral element, the unnorm wll show downward (upward) renforcement. If one of the arguments s larger than the neutral element whle the other argument s smaller (or vce versa), the unnorm wll show compensatory behavor. Ths behavoral versatlty of the unnorm aggregator s one of the man reasons why the unnorm famly was selected as the aggregator to model the customer satsfacton process. Furthermore, unnorms are nterestng to apply n customer satsfacton theory because they match closely wth several customer satsfacton concepts. The domnant model n customer satsfacton research s based on the dsconfrmaton of expectaton paradgm (Olver, 1980, 1997) [8]. Ths model states that customer satsfacton s an addtve combnaton of the expectaton level and the resultng attrbute-level dsconfrmatons. Ths concept dffers from the smple

5 regresson model, whch consders satsfacton as an addtve combnaton of the attrbute performances. In contrast wth smple regresson models, the unnorm aggregator has a better conceptual ft wth Olver s customer satsfacton model. Frst of all, research by Vanhoof et al. has shown that the neutral element of the unnorm s a proxy for the expectaton level of the customer satsfacton process [14]. Secondly, the unnorm aggregator s manly determned by the devaton between the argument and the neutral element (dsconfrmaton), rather than by the absolute value of the argument (attrbute performance). Furthermore, the customer satsfacton aggregaton process s also presumed to be a heurstcs-based decson-makng process [15]. Two heurstcs stand out n ths process: anchorng and adjustment and renforcement. Anchorng and adjustment mples that the consumer assesses the attrbute-level satsfacton scores aganst an ndvdual product-level anchor, whch s hghly complementary to the expectatondsconfrmaton concept and whch s a behavor that can be modeled well by unnorms. Renforcement means that customers ncreasngly exaggerate evaluatons when they fall short of or exceed expectatons, whch s also a behavor that can be modeled by unnorms. It s obvous that unnorms have several behavoral propertes matchng closely wth aspects of the customer satsfacton process, whch provdes theoretcal valdaton for our approach. Therefore, we beleve that unnorms contan a great potental to model customer satsfacton and to derve attrbute mportance measures. 3.2 The unnorm aggregator The unnorm appled n ths research s based on the aggregaton operators presented by Domb [3]. He shows that these operators, as long as they follow the axom system he dscusses, can be wrtten by means of a generator functon f(x), cf Equaton 4. = 1 U ( x1, x2,..., x j ) f f ( x j ) (4) j Furthermore, Domb shows that the generator functon f(x) dsplaced by d, f(x+d) = f d (x), generates a new unnorm wth a dfferent neutral element. Ths mples that one generator functon can generate several unnorms, each wth dfferent neutral elements e. Ths makes t possble to create a unque unnorm, wth a specfc neutral element for each respondent y, based on a sngle unnorm generator functon. The neutral element e y for each respondent can be calculated by Equaton 5. Once the respondents neutral element e y, whch s a proxy for the respondents expectaton level, has been determned, t s possble to calculate A *, whch represents the overall satsfacton for respondent y f no nfluence would have been exerted by attrbute j. The fourth property of the unnorm famly allows us to calculate ths value by replacng attrbute j wth the neutral value for respondent y, as shown n Equaton 6. n 1 1 f ( x ) f ( Ay ) j= 1 e = y f (5) n 1 * A ( 1y ( j 1) y y ( j+ 1) y = U,...,, e,,..., ) (6) Fnally, the mpact I jky can be determned by takng the dfference between the reported satsfacton A y and A *, as shown by Equaton 7. Ths mpact I jky can be postve or negatve and measures the mpact of attrbute j, whch has a performance score of k, on the overall satsfacton of respondent y. * I = A A (7) jky y The mpact measures I jky are calculated at the level of a sngle respondent. However, tradtonal IPA needs nformaton at the populaton level, whch can be obtaned by takng the average of the mpact scores. Because recent research shows that the attrbute mpact s dependent on the attrbute performance, condtonal averages are taken (cf equaton 8). ( I jky = k) I jk = (8) ( number of = k) These mpact averages represent the average mpact of attrbute j on the overall customer satsfacton, when j = k. Fnally, to derve mportance scores, the absolute value of each mpact average I jk has to be taken, because a very large negatve mpact s equally mportant as a very large postve mpact. The IPA needs two coordnates for each attrbute. The frst coordnate s the average attrbute performance P j, whch s determned by takng the arthmetc mean of all attrbute performance scores n the dataset for that specfc attrbute. The second coordnate s the attrbute mportance. We could take the arthmetc mean of all mportance scores I jky and use ts absolute value as the attrbute mportance coordnate. However, ths assumes that the mpact of an attrbute can be represented by a pont-estmate, whch s contradcted by prevous research [8, 9]. = I + P k)( I + I ) (9) I jpj jk ( j j( k 1) jk where k < Pj < k +1 Therefore, Equaton 8 s used, whch determnes the mpact of attrbute j for each possble value k of j. Next, to determne the mpact of attrbute j, when j = P j, the formula n equaton 9 s used, whch s based ny

6 on the technque of nterpolaton. Fnally, the absolute value of I jpj s taken as the mportance coordnate. 3.3 IPA valdaton Past IPA research has manly been focused on extendng the orgnal IPA model [6, 10]. As Oh [10] ponts out, only few studes have crtcally consdered the conceptual valdty of IPA. Recent IPA research [11, 8] and customer satsfacton research [9] have crtcally questoned the usefulness of a smple lnear regresson model to model customer satsfacton. Our emprcal study showed that a smple regresson can ndeed delver based and unrelable results. But also the use of drectly measured attrbute mportance has been questoned [7, 10]. Frstly, drect measurement of attrbute mportance brngs along methodologcal dscussons, lke e.g. the use of unvarate versus bvarate measurement scales. Furthermore, Oh ponts out that drect mportance measurement of one attrbute at a tme s lkely to nflate mportance ratngs, hereby restrctng the varaton. Fnally, Matzler et al. clam that drectly measured attrbute mportance represents the overall attrbute mportance nstead of the attrbute mportance related to the attrbute s current performance level. The performance related attrbute mportance, whch s more useful n IPA analyss, can dffer greatly from the overall mportance. However, despte the questonable valdty of the exstng IPA technques, IPA has become an mportant and wdely accepted manageral tool and should not be dscarded as a whole. Yet, ths leaves us n a nearly mpossble poston to valdate our results drectly because no 100% vald technque exsts to measure or derve the true attrbute mportance. Therefore, we are lmted to valdatng the underlyng customer satsfacton modelng approach whch s the foundaton of our mportance measures. Secton 3.1 already addressed the theoretcal valdaton of unnorms to model customer satsfacton. It was shown that a theoretcal match exsts between the unnorm s propertes and customer satsfacton behavor. In addton to the theoretcal valdaton, further emprcal valdaton s requred, whch can be provded by comparng our results wth the conclusons from Szymansk and Henard s meta-analyss of 85 exstng customer satsfacton studes [13]. A substantal part of ther paper focuses on the relatonshps between customer satsfacton and several of ts antecedents. Table 5 shows the results of Szymansk and Henard, compared wth our results. Our results closely follow the emprcal results from other customer satsfacton research, ndcatng an emprcal match between the unnorms behavor and the customer satsfacton behavor. All these results, both theoretcal and emprcal, provde evdence that unnorms are able to model customer satsfacton, whch ndrectly supports our unnorm IPA approach. Table 5 Emprcal valdaton Szymansk and Henard Postve Negatve Correlatons Correlatons Our results Postve Correlatons Negatve Correlatons Expectaton* Satsfacton Dsconfrmaton** Satsfacton Expectaton* Performance NOTE I Only statstcally sgnfcant correlatons at alpha.05 were consdered. NOTE II Expectaton, dsconfrmaton and performance are measured or derved for each company at attrbute level. * expectaton = unnorm s neutral element. ** dsconfrmaton = performance expectaton. 3.4 Case study The purpose of ths case study s to llustrate the applcaton of the unnorm-based IPA approach. Fgure 1 shows the IPA for the frst company n our dataset. The postonng of the -axs (Y-axs) s based on the center of the hghest and the lowest x (y) coordnates. Other ways of postonng the axes exst, e.g. takng the average of the x (y) coordnates of all attrbutes as cutpont for the Y-axs (-axs). However, the man pont of an IPA analyss s the relatve postonng of the attrbutes, rather than the absolute postonng [6]. Importance 0,43 0,38 0,33 0,28 0,23 0,18 0,13 0,08 Fg. 1 Unnorm based IPA IPA (Unnorm based mpact) 0,03 7,72 7,92 8,12 8,32 8,52 Perform ance Analyss of ths grd shows that attrbutes 1, 4 and 6 fall n the upper rght quadrant, where both performance and mportance are hgh. Ths s the Keep up the good work zone. Attrbutes 5 and 7 are located n the lower left quadrant. These attrbutes have a low performance, but are also low n mportance. Ths area s called the Low prorty zone. Attrbutes 2 and 3 le _1 _2 _3 _4 _5 _6 _7

7 n the upper left quadrant or the Concentrate here zone, where the mportance s hgh but the performance s low. Fnally, the lower rght quadrant, whch s the Possble overkll zone, s empty. Ths type of analyss allows the manager to formulate a strategy to enhance customer satsfacton. Based on the IPA of Fgure 1, the company should concentrate on attrbutes 2 and 3, whle mantanng efforts on 1, 4 and 6. 4 Conclusons Importance-Performance Analyss s an mportant manageral marketng tool. However, as shown n our emprcal study, the smple regresson model, often used to determne the attrbutes mportance scores, has ts problems. Further research on the nature of and solutons to these problems are necessary. In ths work, we presented an alternatve approach, based on unnorm aggregators, to determne attrbute mportance measures. Frstly, the unnorm based approach calculates mpact measures at the level of a sngle respondent. Even when averagng these mpact measures, to obtan populaton level fgures, we preserve the beneft of populaton level mpact scores whch are condtonal to the performance score. Secondly, the unnorm approach mplctly takes nteracton effects nto account and focuses on dsconfrmaton nstead of attrbute performance, allowng a close match wth exstng customer satsfacton models. Furthermore, because of ts propertes lke compensatory behavor, renforcement behavor and the neutral element as anchor, the unnorm approach matches consderably well wth the theoretcal fundamentals of customer satsfacton theory. Besdes the theoretcal valdaton, we also provded emprcal valdaton for the use of unnorms n a customer satsfacton context. In short, the use of aggregaton operators, such as the unnorm, possesses a great deal of potental as a novel technque n the feld of customer satsfacton research and Importance-Performance Analyss. The ntegraton of unnorms n IPA, as performed n ths artcle, should be consdered as a prelmnary study of the unnorm s applcablty n ths specfc marketng feld. References: [1] Detyneck, M, Fundamentals on aggregaton operators. Ths manuscrpt s based on Detyneck s doctoral thess and can be downloaded from [2] Dolnsky, A.L., Caputo, R.K., Addng a compettve dmenson to mportance-performance analyss: An applcaton to tradtonal health care systems, Health Marketng Quarterly, Vol. 8, No. 3/4, 1991, pp [3] Domb, J., Basc concepts for the theory of evaluaton: The aggregatve operator, European Journal of Operatonal Research, Vol. 10, 1982, pp [4] Dubos, D. Prade., H., On the use of aggregaton operatons n nformaton fuson processes, Fuzzy Sets and Systems, Vol. 142, 2004, pp [5] Gujarat, D.N., Basc Econometrcs, McGraw-Hll, Inc., [6] Martlla, J.A., James, J.C., Importance-performance analyss, Journal of Marketng, Vol. 41, No. 1, 1977, pp [7] Matzler, K., et al., Importance-performance analyss revsted: The role of the factor structure of customer satsfacton, The Servce Industres Journal, Vol. 23, No. 2, 2003, pp [8] Matzler, K., et al., The asymmetrc relatonshp between attrbute-level performance and overall customer satsfacton: a reconsderaton of the mportance-performance analyss, Industral Marketng Management, Vol. 33, No. 4, 2004, pp [9] Mttal, V., et al., The asymmetrc mpact of negatve and postve attrbute-level performance on overall satsfacton and repurchase ntentons, Journal of Marketng, Vol. 62, No. 1, 1998, pp [10] Oh, H., Revstng mportance-performance analyss, Toursm Management, Vol. 22, 2001, pp [11] Sampson, S.E., Showalter, M.J., The performancemportance response functon: Observatons and mplcatons, The Servce Industres Journal, Vol. 19, No. 3, 1999, pp [12] Slack, N., The mportance-performance matrx as a determnant of mprovement prorty, Internatonal Journal of Operatons & Producton Management, Vol. 14, No. 5, 1994, pp [13] Szymansk, D.M., Henard D.H., Customer satsfacton: A meta-analyss of the emprcal evdence, Journal of the Academy of Marketng Scence, Vol. 29, No. 1, 2001, pp [14] Vanhoof, K., et al., An ndrect measurement for customer expectaton, Prncples of Fuzzy Preference Modellng and Decson Makng, Academa Press, 2003, pp [15] Vanhoof K., et al., Penalty-Reward Analyss wth Unnorms: A Study of Customer (Ds)Satsfacton, INTELLIGENT DATA MINING. Technques and Applcatons, Sprnger, 2005, pp [16] Yager, R.R., Rybalov, A., Unnorm aggregaton operators, Fuzzy Sets and Systems, Vol. 80, 1996, pp