Progress in Business Innovation & Technology Management. Analysis of Hotel Service Quality Perceptions Using Fuzzy TOPSIS

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1 Progress in Business Innovtion & Technology Mngement Contents lists ville t ProBITM Progress in Business Innovtion & Technology Mngement PBITMS Homepge: nlysis of Hotel Service Qulity Perceptions Using Fuzzy TOPSIS Yi-Li Cheng Yun-Hsu Lin* nd Ming-Lng Tseng Deprtment of Informtion Mngement WuFeng University Tiwn Deprtment of Finnce MingDo University Tiwn E-mil:yunhsu@mdu.edu.tw Grdute School of Business nd Mngement LungHw University of Science nd Technology BSTRCT Content this study pplies n evlution pproch on ssessing perceived service qulity sed on the Technique for Order Performnce y Similrity to Idel Solution TOPSIS. Two study groups comprise this reserch nmely customers nd employees. This study includes 5 evlution criteri ssessed y nd employees nd customers from the four hotels in Tiwn. The use of tringulr fuzzy numers TFNs hndles the vgueness nd sujectivity inherent in the gthered linguistic informtion. This study pplies TOPSIS method to the importnce weights of evlution criteri nd to synthesize the rtings of the studied hotels in fuzzy environment. The study result otins crisp overll performnce vlue for ech hotel to mke finl comprison etween the perceptions of the two reserch groups. 0 PBITM Society. ll rights reserved. Keywords: Fuzzy set theory TOPSIS service qulity I. Bckground Price nd service qulity remins s the primry competitive wepons ecuse hotels relize tht competition on price lone represents no-win sitution in the long run. Some hotels now tend to focus on improving customer service Berry Prsurmn nd Zeithml 988 for evidence suggest the importnce service qulity plys in firm s competitive dvntge Fitzsimmons nd Fitzsimmons 994. Service qulity mesurement provides ssessments of service performnce service prolems service delivery; such ssessments serve s sis for employee nd corporte rewrds Prsurmn 995. However discrepncy in the perceived service qulity etween customers nd employees occurs nd Emil: yunhsu@mdu.edu.tw

2 might incur unstisfctory customer service. s n on-going process hotel service qulity evlution in the hotel industry requires continuous monitoring to mintin its high levels cross numer of service criteri. With the rpid growth of lterntive hotels hotel mngement needs to tke importnt steps to improve customer stisfction. Consequently hotels should lso consider consolidting their mrket shres nd enhnce profitility to compenste for the cost of this ssessment. This study tkes motivtion from Sultn nd Simpson 000; their study investigtes service qulity perceptions nd expecttions of Europen nd mericn pssengers of Europen nd United Sttes US irline crriers. Similrly reserch y Cunninghm et l. 00 focusing on the perceptions of pssengers coming from two countries reports significnt differences in service qulity perceptions etween Koren nd US irline pssengers. Vrious studies on service qulity emphsize its dimensions wheres nlysis of perceived service qulity in the hotel industry is limited. However customer perceptions of service experiences re vitl to the success of ll service orgniztions. It is generlly understood tht customer perceptions re usully judged y humn perception mesurement. Humn judgment in socil science is lwys represented s exct numers. In mny prcticl cses the humn preference model is uncertin nd customer expecttion might e reluctnt or unle to ssign exct numericl vlues to descrie the preferences Chen nd Tzeng 00; Tseng et l Since some of the evlution criteri re sujective nd qulittive in nture descried in linguistic informtion it is very difficult for the customer to express the preferences using exct numericl vlues nd this result more desirle for the reserchers to use fuzzy logic evlution. Unfortuntely there re few studies to evlute the service qulity in environment uncertinty To solve this issue the fuzzy environment uncertinty sujectivity imprecision nd miguity chrcterizes the criteri used to mesure service qulity. Consumers usully employ this sujective knowledge nd linguistic informtion when mking decisions. The use of TFNs to represent linguistic terms nd fcil expressions for the sujective ssessment reduces the cognitive urden in the survey process. The developed lgorithm effectively ggregtes the ssessment of the respondents to ech criterion y using n overll fuzzy numer tht cptures the importnce of the criteri sed on the opinion of the respondents y ssigning vlues to them. This study pplied the TOPSIS proposed y Hwng nd Yoon 98 the logic of TOPSIS is to define the idel solution nd negtive idel solution. The idel solution is to mximize the cost criteri nd minimize the enefit criteri. In short the idel solution consists of ll of est vlues ttinle of criteri wheres the negtive idel solution is composed of ll worst vlues ttinle of criteri. The optiml lterntive is the one which hs the shortest distnce from the idel solution nd the frthest distnce from the negtive idel solution ses on the TOPSIS concept of the degree of optimlity provides the rnking of the four hotels y oservtion group. There re four merits to propose this pproch: the logic is reltionl nd understndle; the computtion processes is strightforwrd; the concept permits to pursuit the est lterntives for ech criteri depicted in simple mthemticl form nd 4 the importnce weights re incorported into the comprison processes Olson 004. With these merits this study is utilized multi criteri decision mking MCDM method to determine the importnce weights of evlution criteri nd TOPSIS to otin the performnce rtings of the fesile lterntives in linguistic 9

3 terms prmeterized with tringulr fuzzy numers Jhnshhloo et l. 005; Wng nd Lee 007; Wng nd Chng 007. This study ims to mesure the gp in the perception of employees nd customers on service qulity in uncertinty. This nlysis consists of ppliction method to mesure hotel service qulity nd enumerting the evlution criteri to e considered when evluting hotel service qulity in fuzzy environment. Hence this study contriutes to literture minly y its evlution of the differences etween hotel s customer nd employee estlishments in uncertinty. The nlyticl results show n overll comprison of service qulity criteri cross the two groups in uncertinty. The findings offer opportunities to identify opertionl res to e improved. This section egins with n introduction to the issues relevnt to service qulity in hotels. The reminder of this study is structured s follows: Section presents the literture review. Section discusses the reserch method. Section 4 provides n empiricl study nlysis. Section 5 contins the conclusion nd the future direction of the reserch. II. Literture Review To success mnging the chllenges of gloliztion nd intensive competitition firms need to notify the service qulity expecttion. The service qulity perceptions hve een received extensive ttention from reserchers nd prctitioners. In recent decdes sustntil literture exmines the concept of service qulity its dimensions nd mesurement methods. For Grönroos 984 the perceived qulity of given service will e the result of n evlution process where the consumer compres his expecttions with his perception of the service qulity received. Grönroos plces the perceived service nd the expected service opposite one nother. His reserch pioneers the proposl of hving three dimensions nmely technicl qulity functionl qulity nd imge. On the other hnd some uthors propose mesuring service qulity y evluting perceptions nd expecttions jointly Brown Churchill nd Peter 99. Most reserch on ccommodtion services focus on hotels without prticulr reference to the perception comprison etween customers nd employees Sleh nd Ryn 99 99; Getty nd Thompson 994; Ptton Stevens nd Knutson 994; Suh Lee Prk nd Shin 997; Benitez Mrtin nd Romn 007. Criteri need specific definitions in the evlution of the qulity of service. Numerous studies ttempt to estlish which criteri or fctors to consider when evluting service qulity. mong these the reserch y Prsurmn Zeithml nd Berry 985 ers greter impct nd identifies ten dimensions which were susequently reduced to five 988 nmely tngile reliility response ssurnce nd empthy. t present no consensus exists on the numer of dimensions or their pplicility to which services. For exmple the study of Crmn 990 investigtes different types of services nd suggests tht the dimensions proposed y Prsurmn Zeithml nd Berry 988 re not pplicle to every type of service nd tht other dimensions exist such s convenience nd cost. He lso disgrees with the wy tht the initil dimensions were comined into five. This shows the difficulty of quntifying service qulity ecuse of the very nture of service itself. Berry Prsurmn nd Zeithml 988 nd Prsurmn Zeithml nd Berry stte tht service qulity ssessment results while customers compre their service qulity expecttions to their 9

4 perception of received service. This definition points out the significnt impct of employee performnce on customers perception of service qulity. Linguistic informtion usully ppers s n importnt output of service qulity engineering prolems. This informtion is more difficult to mesure throughout clssicl mthemticl function ecuse linguistic informtion represents sujective knowledge tht is usully overlooked y nlysts when forming mthemticl models tht depicts rel world phenomen. In mrketing reserch most questionnires use Likert scles to mesure respondents linguistic ttitude. Previous studies employ sttisticl methods to nlyze the qulity of service in the hotel industry using some n-point Likert scle to weigh the importnce of different criteri. common pproch pplies the fuzzy set theory. This methodology dequtely overcomes the miguity of concepts ssocited with humn eing s sujective judgments. The fuzzy set theory finds vrious pplictions in the field of mngement science Hutchinson 998; Xi Wng nd Go 000 nd egins to gin cceptnce in the field of service qulity Tsur Chng nd Yen 00; Yeh nd Kuo 00. Building from surveys nd n extensive cse study Berry et l. 988 shows reliility s the most importnt fctor to consumers. Usully studies mesure ttriutes to descrie the five constructs enumerted. Respondents nswer two sets of questionnire; the first ssesses ll ttriutes sed on service expecttions wheres the second ssesses the sme ttriutes sed on perceptions of received service. Hence mesuring service qulity y compring customers expecttions nd perceptions over the ttriutes requires two-stge evlution from respondents. The customer s comprison of their normtive expecttions for wht should hppen in service encounter with perceptions of wht ctully hppened represents the level of perceived service qulity received y customer Prsurmn Zeithml nd Berry 988; Zeithml Berry nd Prsurmn 99. These normtive expecttions nd susequent comprisons re mde cross vriety of service ttriutes pertining to numer of service dimensions. This reserch follows the stndrd service qulity definition shown in Tle to develop criteri for decision mking in hotel opertions in uncertinty. To success mnging the chllenges of gloliztion nd intensive competitition firms need to notify the service qulity expecttion. The service qulity perceptions hve een received extensive ttention from reserchers nd prctitioners. In recent decdes sustntil literture exmines the concept of service qulity its dimensions nd mesurement methods. For Grönroos 984 the perceived qulity of given service will e the result of n evlution process where the consumer compres his expecttions with his perception of the service qulity received. Grönroos plces the perceived service nd the expected service opposite one nother. His reserch pioneers the proposl of hving three dimensions nmely technicl qulity functionl qulity nd imge. On the other hnd some uthors propose mesuring service qulity y evluting perceptions nd expecttions jointly Brown Churchill nd Peter 99. Most reserch on ccommodtion services focus on hotels without prticulr reference to the perception comprison etween customers nd employees Sleh nd Ryn 99 99; Getty nd Thompson 994; Ptton Stevens nd Knutson 994; Suh Lee Prk nd Shin 997; Benitez Mrtin nd Romn 007. Criteri need specific definitions in the evlution of the qulity of service. Numerous studies ttempt 9

5 to estlish which criteri or fctors to consider when evluting service qulity. mong these the reserch y Prsurmn Zeithml nd Berry 985 ers greter impct nd identifies ten dimensions which were susequently reduced to five 988 nmely tngile reliility response ssurnce nd empthy. t present no consensus exists on the numer of dimensions or their pplicility to which services. For exmple the study of Crmn 990 investigtes different types of services nd suggests tht the dimensions proposed y Prsurmn Zeithml nd Berry 988 re not pplicle to every type of service nd tht other dimensions exist such s convenience nd cost. He lso disgrees with the wy tht the initil dimensions were comined into five. This shows the difficulty of quntifying service qulity ecuse of the very nture of service itself. Berry Prsurmn nd Zeithml 988 nd Prsurmn Zeithml nd Berry stte tht service qulity ssessment results while customers compre their service qulity expecttions to their perception of received service. This definition points out the significnt impct of employee performnce on customers perception of service qulity. Linguistic informtion usully ppers s n importnt output of service qulity engineering prolems. This informtion is more difficult to mesure throughout clssicl mthemticl function ecuse linguistic informtion represents sujective knowledge tht is usully overlooked y nlysts when forming mthemticl models tht depicts rel world phenomen. In mrketing reserch most questionnires use Likert scles to mesure respondents linguistic ttitude. Previous studies employ sttisticl methods to nlyze the qulity of service in the hotel industry using some n-point Likert scle to weigh the importnce of different criteri. common pproch pplies the fuzzy set theory. This methodology dequtely overcomes the miguity of concepts ssocited with humn eing s sujective judgments. The fuzzy set theory finds vrious pplictions in the field of mngement science Hutchinson 998; Xi Wng nd Go 000 nd egins to gin cceptnce in the field of service qulity Tsur Chng nd Yen 00; Yeh nd Kuo 00. Building from surveys nd n extensive cse study Berry et l. 988 shows reliility s the most importnt fctor to consumers. Usully studies mesure ttriutes to descrie the five constructs enumerted. Respondents nswer two sets of questionnire; the first ssesses ll ttriutes sed on service expecttions wheres the second ssesses the sme ttriutes sed on perceptions of received service. Hence mesuring service qulity y compring customers expecttions nd perceptions over the ttriutes requires two-stge evlution from respondents. The customer s comprison of their normtive expecttions for wht should hppen in service encounter with perceptions of wht ctully hppened represents the level of perceived service qulity received y customer Prsurmn Zeithml nd Berry 988; Zeithml Berry nd Prsurmn 99. These normtive expecttions nd susequent comprisons re mde cross vriety of service ttriutes pertining to numer of service dimensions. This reserch follows the stndrd service qulity definition shown in Tle to develop criteri for decision mking in hotel opertions in uncertinty. 94

6 ss Tle The five dimension of service qulity s defined y Prsurmn et l.988 Dimension Description Reliility The ility to perform the promised service dependly nd ccurtely Tngiles The ppernce of physicl fcilities equipment personnel nd communiction mterils Responsivene The willingness to help customers nd provide prompt service ssurnce The knowledge nd courtesy of employees nd their ility to convey trust nd confident Empthy The cring individulized ttention provided to the customer. This preliminry literture reviewed illustrtes the fct tht customer perceptions of service qulity re criticlly importnt for the success of hotels. However the service qulity is lcking of the considertion of environment uncertinty nd there is none study presents such fuzzy environment in mrketing reserch. With this ckground this study extrpolte prior results relted to mrketing reserch in the new context of hotels nd ct on modified SERVQUL for finding the gp etween customer s expecttion nd employee s performnce descried in linguistic informtion. III. Methodologies This section detils the steps in opertionlizing service qulity s Prsurmn et l. 985 define. The method includes exmining completed questionnires 5 questions. Two sets of linguistic terms very low low medium high very high; very poor poor fir good very good re used for ssessing service qulity with respect to ech criterion. Ech respondent from different groups ssesses the performnce rting of ech criterion y using one of the linguistic terms defined in the corresponding term set. The respondent lso needs to tick off elow one of the expressions of the fces for ech evlution criteri. Tle presents the mesurement criteri for this study the criteri re sed on the interviewed with the hotels nd prior studies Prsurmn et l. 988; Prsurmn et l

7 . Smpling methods of customer nd employee s groups crucil considertion in dministering surveys is the ppropriteness of the questions. Up to now most reserches relte to service qulity primrily focused on whether the questionnires or the difference scores of sttisticl results re vlid nd resonle Tes 99; Bkus nd Boller 99; Dholkr et l In ddition their mesurement minly relies on sttisticl methods or reserched smple elonging to the sme type of smpling method. In contrst to these this study uses TOPSIS method nd comined with fuzzy set theory nd the informtion collects from the two study groups. totl of 6 responses were otined during the four-month period following the distriution of the questionnires. Discounting the numer of invlid questionnires only surveys were used for the finl nlysis. Gthering dt through the survey helped support scle generliztion for hotels Bie 998. Therey the modified instrument usully mny socil science prolems re involving imprecision constrints nd possile ctions re not precisely in description Bellmn nd Zdeh 970. The reserch result in uncertin environment is highly ffected y sujective judgments tht re vgue nd imprecise. To solve this kind of imprecision prolem fuzzy logic ws first introduced y Zdeh 965 s mthemticl 96

8 wy to represent nd hndle vgueness in decision-mking. In fuzzy logic ech numer etween 0 nd indictes prtil truth wheres crisp sets correspond to inry logic [0 ]. Hence fuzzy logic cn express nd hndle vgue or imprecise judgments mthemticlly l-njjr & lsyouf 00. To del with the vgueness of humn thought nd expression in mking decisions fuzzy logic is very helpful. In prticulr to tckle the miguities involved in the process of linguistic estimtion it is eneficil wy to convert these linguistic terms into fuzzy numers..fuzzy sets theory This study uilds on some importnt definitions nd nottions of fuzzy set theory from Chen 996 Cheng nd Lin 00. X={x x x.x n } designtes the universe of discourse. Fuzzy set of X is set of ordered pirs { x f x x f x... x f x n n } where f : X [0] represents the memership function of nd f x i stnds for the memership degree of x i in. The following definitions pply in this study: Definition. When X is continuous rther thn countle or finite set the fuzzy set is denoted s X f xi / x where x X. Definition. When X is countle or finite set the fuzzy set is represented s f i xi / xi where x i X. Definition. fuzzy set of the universe of discourse X is norml when its memership function f x stisfies mx f x. Definition 4. fuzzy numer is fuzzy suset in the universe of discourse X tht is not convex ut is norml. Definition 5. The fuzzy α-cut is defined y { xi f x x X} i i { x f x x X} i i i nd strong α-cut where where [0] [0] of the fuzzy set in the universe of discourse X Definition 6. fuzzy set of the universe of discourse X is convex if nd only if every is convex 97

9 98 tht is is close intervl of R. This definition cn e written s [0] ] [ where P P Definition 7. TFN cn e defined s triplet ; the memership function of the fuzzy numer s defined is shown in Fig.. 0 / / 0 x x x x x x x f ssigning nd B to e two TFN prmeterized y the triplet nd respectively the opertionl lws of these two TFN re s follows: / / / B B B B 4 x f 0 X Figure Memership function of Tringulr Fuzzy Numer The vertex method y Chen 000 clcultes the distnce etween TFN nd B s follows: [ B d 5. Fuzzy TOPSIS derivtion of the crisp overll performnce vlues of lterntives

10 In fuzzy TOPSIS most of the steps of TOPSIS re esily generlized to fuzzy environment. Since TOPSIS is well-known method for clssicl MCDM mny reserchers hve pplied TOPSIS to solve MCDM prolems in the pst. This study defuzzify fuzzy rtings nd weights into crisp vlues the fuzzy TOPSIS is stted s follows: Suppose tht decision group hs k memers. k w j represents the fuzzy weight of jth criterion ssessed y k evlutors. pplying the synthetic vlue nottion integrtes the different opinions of evlutors. This procedure ggregtes the sujective judgment for k evlutors given y... k wj wj wj wj wj k 6 Hwng nd Yoon 98 originlly propose the TOPSIS. This proposition requires the chosen lterntive to hve not only the shortest distnce from the positive idel reference point PIRP ut lso the longest distnce from the negtive idel reference point NIRP to solve MCDM prolems o-sinn nd mer 004 Wng nd Chng 005. The study pplies the method of Chen 000 to otin ech lterntive s overll performnce vlue using linguistic fuzzy tringulr numers. The lgorithms of this method re descried s follows. Step : Construct the fuzzy decision mtrix - Given m lterntives criterion nd k decision-mkers typicl fuzzy multi-criteri group decision mking prolem cn e express in mtrix formt s in 7. C C C n D... m X X... X m X X... X m X n X n i... m; j... n... X mn 7 In 7 m represent the lterntives to e chosen C C..C n denote the evlution criteri x expresses the rting of lterntive i with respect to criteri C j ssessed y k evlutors concerning the sme evlution criteri tht is x x x x k... x k 8 where k x is the rting of lterntive i with respect to criterion C j evluted y kth evlutor nd k k k x k c. Step : Normlize the fuzzy decision mtrix Normlizing the rw dt elimintes nomlies with different mesurement units nd scles in severl MCDM prolems. However the liner scle normliztion function 99

11 pplied here preserves the property tht the rnges of normlized TFNs to e included is [0 ]. Therefore in the normlized fuzzy decision mtrix R r i... m; j... n mxn 9 where r c j c j c c j r 0 c j mx c i Step : Construct weighted normlized fuzzy decision mtrix - Considering the different weight of ech criterion otin the weighted normlized decision mtrix y multiplying the importnce weights of evlution criteri nd the vlue in the normlized fuzzy decision mtrix. The weighted normlized decision mtrix V is defined s V v i... m; j n... mxn v r w j where w j represents the importnce weight of criterion C j. Step 4: Determine the FPIRP nd FNIRP - The positive TFNs re included in the intervl [0]. Hence the following definition of fuzzy positive idel reference point FPIRP + nd fuzzy negtive idel reference point FNIRP - pplies: v v... vn v v... v n 4 where v j = nd v j = j=..n. Step 5: Clculte the distnces of ech lterntive to FPIRP nd FNIRP - The following derives the distnce of lterntive from FPIRP nd FNIRP: 00

12 d i n j d v v j d i n j d v v j i... m; j... n 5 respectively where d v v denotes the mesured distnce etween two fuzzy numers di represents the distnce of lterntive i from FPIRP nd d i is the distnce of lterntive i from FNIRP. Step 6: Otin the closeness coefficient nd rnk the order of lterntives - The rnking order of ll lterntives cn e otined once the closeness coefficient is determined. This method llows the decision mkers to select the most fesile lterntive. The closeness coefficient of ech lterntive is clculted s di CCi i... m d d i i 6 n lterntive with index CC i pproching first indictes tht the lterntive is close to the FPIRP nd fr from the FNIRP. This sttement mens tht lrge vlue of index CC i indictes good performnce of the lterntive i. IV. Empiricl Result The hotels Tiwn sed prticipting in this study re listed in the 006 English evlution of est hotels nmely GC hotel CC Hotel UH hotel nd TF hotel. The empiricl result follows the step y step reserch method s follows: Customer spect: clculte the synthesized importnce weights of evlution criteri The questionnires contin the opinion of the respondents on the level of importnce of ech evlution criterion using linguistic vriles sed on the linguistic scles nd corresponding TFN Tle. This study utilizes the est non-fuzzy performnce BNP vlue to defuzzify the TFN nd to understnd the importnce order of the criteri. Employing the verge vlue descried in Eq. 8 genertes the integrted fuzzy importnce weight mtrix for evlution criteri Tles 4 nd 5. The BNP vlues Tle 4 revel the five most importnt performnce criteri for initil perceived service qulity s follows: the employees re pprochle nd esy to contct 0.8 the physicl fcilities nd employees re net nd clen 0.80 the employees consider the individul needs of the customers nd offer them personlized service 0.80 the fcilities re ville t convenient hours 0.69 nd the employees re courteous polite nd respectful

13 0

14 . Results The five most importnt performnce criterion considering employee spects Tle 5 re s follows: the employee re pprochle nd esy to contct 0.79 the physicl fcilities nd employees re net nd clen 0.78 the employees listen to me nd spek in lnguge tht I cn understnd 0.78 the fcilities re ville t convenient hours 0.76 the employees re competent i.e. Knowledgele nd skillful 0.75 nd the fcilities provide n environment tht is free from dnger Step : Construct the fuzzy decision mtrix considering Customer spect Breking down service qulity into its constituent evlution criteri fcilittes its simplifiction. This study gives ssessors the generl crisp evlution criteri from Prsurmn et l. 988 s developed y the reserchers. The evlutors dopt linguistic terms Tle 6 including very poor poor fir 0

15 good nd very good to express their opinions out the respondent perception on ech performnce criteri sed on the perception of the two respondent groups listed in Tle. Eqution 6 gives the verge fuzzy performnce rtings of ech hotel with respect to the evlution criteri to synthesize the linguistic informtion nd vrious individul judgments. The synthesized fuzzy decision mtrix cn e computed s in Tle 7. Step : Normlize the fuzzy decision mtrix pplying equtions 9- utilizes liner scle trnsformtion functions to ensure tht the normlized TFN remins in the intervl [0 ]. Tle 7 shows the synthetic fuzzy decision mtrix for the customer group. For instnce the mximum fuzzy numer listed in the first row of Tle 7 is 9.0. The normlized vlues re the fuzzy numers shown in the first row divided y 9.0. Normlizing the other 5 rows follows the sme procedure. 04

16 05

17 06

18 Step : Estlish the weighted normlized fuzzy decision mtrix Following equtions nd gives the weighted normlized fuzzy decision mtrix. For exmple the fuzzy numer of lterntive S with respect to criteri Tle 9 re 0.9 = 0.4 x

19 0.4 = 0.6 x 0.69 nd 0.7= 0.8 x 0.9 respectively. Step 4: Determine the fuzzy positive nd negtive idel reference points The positive TFNs re within the rnge [0 ]. The FPIRP nd FNIRP re defined s: + = [ ]; - = [ ] Step 5: Clculte the distnce of ech lterntive to FPIRP nd FNIRP Following equtions 5 nd 5 gives the distnce of ech lterntive to the FPIRP nd FNIRP Tle. d + ={[ ]/} 0.5 +{[ ]/} {[ ]/} {[ ]/} 0.5 =0.86 d - ={[ ]/} 0.5 +{[ ]/} {[ ]/} {[ ]/} 0.5 =.4 Step 6: Otin the closeness coefficient for rnking the four lterntives Customer spect Following eqution 6 provides the closeness coefficient. The index CC for the first lterntive hotel is clculted s CC =.4/ =0.7. n lterntive with closeness coefficient close to hs the shortest distnce from the FPIRP nd lrgest distnce from FNIRP. lrge closeness coefficient of n lterntive indictes good performnce. Tle shows the closeness coefficient of the four lterntives. The customer spect rnking of the four hotels re s follows: Customer spect: S 0.7>S 0.705>S 0.689>S Repeting the computtions enumerted for the employee dt gives the closeness coefficient of the four lterntives. Results Tle differ from the customer spect. Hotel employee s spect: S 0.74>S 0.70>S 0.708>S

20 REFERENCES dler N. Friedmn L. Sinuny-Stern Z. 00 Review of rnking methods in the dt envelopment nlysis context. Europen Journl of Opertionl Reserch ndersen P. Petersen N.C. 99 procedure for rnking efficient units in dt envelopment nlysis. Mngement Science