A successful indirect method to calculate the importance of the attributes in services is that of correlation between the performance of attributes and the overall satisfaction such as they are perceived by customers. Often, in practice, the input data must be considered as fuzzy numbers, therefore it is completely justified our aim in the present paper, to give an indirect method of calculation of the importance of attributes in the fuzzy case, based on the correlation coefficient. The main benefits are related especially with the importance-performance analysis and multicriteria decision making methods. The effective computation is based on the Zadeh’s extension principle. The expected value, as a very simple and with suitable properties characteristic associated to a fuzzy number, is used for defuzzification and an immediate interpretation of the results. A practical method, algorithms and illustrative examples are given. The results of a survey with respect to the quality of hotel services in Oradea (Romania) are processed in accordance with our method.
AbaloJ., VarelaJ. and ManzanoV., Importance values for importance-performance analysis: A formula for spreading out values derived from preference rankings, Journal of Business Research60 (2007), 115–121.
2.
AkyarE., AkyarH. and DüzceS.A., Fuzzy risk analysis based on a geometric ranking method for generalized trapezoidal fuzzy numbers, Journal of Intelligent and Fuzzy Systems25 (2013), 209–217.
3.
AzzopardiE. and NashR., A critical evaluation of importance-performance analysis, Tourism Management35 (2013), 222–233.
4.
BaconD.R., A comparison of approaches to importance-performance analysis, International Journal of Marketing Research45 (2003), 55–71.
5.
BanA., Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval, Fuzzy Sets and Systems159 (2008), 1327–1344.
6.
BanA., BrândaşA., CoroianuL., NegruţiuC. and NicaO., Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value, Computers and Mathematics with Applications61 (2011), 1379–1401.
7.
BanA. and BanO., Optimization and extensions of a fuzzy multicriteria decision making method and applications to selection of touristic destinations, Expert Systems with Applications39 (2012), 7216–7225.
8.
BanA.I. and CoroianuL., Simplifying the search for effective ranking of fuzzy numbers, IEEE Transactions on Fuzzy Systems23 (2015), 327–339.
9.
BanO.I., (2011)Fuzzy multicriteria decision making method applied to selection of the best touristic destinations, International Journal of Mathematical Models and Methods in Applied Science5 (2014), 264–271.
10.
BanO.I. and BogdanV., Using partial correlation coefficient to assess the importance of quality attributes, Study case for tourism Romanian consumers, International Journal of Social Science and Humanity1 (2013), 21–24.
11.
BanO.I. and MeşterI.T, Using Kano two dimensional service quality classification and characteristic analysis from the perspective of hotels’ clients of Oradea, Journal of Tourism-Studies and Research in Tourism18 (2014), 30–36.
12.
BedeB., Mathematics of fuzzy sets and fuzzy logic, Springer, Studies in Fuzziness and Soft Computing, Heidelberg, New York, New York, 2013.
13.
ChenS.M., (1996)Evaluating weapon systems using fuzzy arithmetic operations, Fuzzy Sets and Systems77 , 265–276.
14.
ChengQ., GuoJ.J. and LingS., Fuzzy importance-performance analysis of visitor satisfaction for theme park: The case of Fantawild Adventure in Taiwan, China, Current Issues in Tourism, 2013 in press. doi:10.1080/13683500.2013.777399
15.
ChiangD.A. and LinN.P., Correlation of fuzzy sets, Fuzzy Sets and Systems102 (1999), 221–226.
16.
ChienC.J. and TsaiH.H., Using fuzzy numbers to evaluate perceived service quality, Fuzzy Sets and Systems116 (2000), 289–300.
17.
ChiouH.K., TzengG.H. and ChengD.C., Evaluating sustainable fishing development strategies using fuzzy MCDM approach, Omega33 (2005), 223–234.
18.
ChuR., Stated-importance versus derived-importance customer satisfaction measurement, Journal of Services Marketing16 (2002), 285–301.
19.
ChuT-C and LinY., An extension to fuzzy MCDM, Computers and Mathematics with Applications57 (2009), 445–454.
20.
DengW.J. and PeiW., Fuzzy neural based importanceperformance analysis for determining critical service attributes, Expert Systems with Applications36 (2009), 3774–3784.
21.
DengW-J, Fuzzy importance-performance analysis for determining critical service attributes, International Journal of Service Industry Management19 (2008), 252–270.
22.
DengW., Using a revised importance-performance analysis approach: The case of Taiwanese hot springs tourism, Tourism Management28 (2007), 1274–1284.
23.
DengY., ChanF.T.S., WuY. and WangD., A new linguistic MCDM method based on multiple-criterion data fusion, Expert Systems with Applications38 (2011), 6985–6993.
24.
DiamondP. and KloedenP., Metric Spaces of Fuzzy Sets. Theory and Applications, World Scientific, Singapore, 1994.
25.
DuboisD. and PradeH., Operations on fuzzy numbers, International Journal of Systems Science9 (1978), 613–626.
26.
DuboisD. and PradeH., The mean value of a fuzzy number, Fuzzy Sets and Systems24 (1987), 279–300.
27.
EbrahimnejadA. and VerdagayJ.L., A novel approach for sensitivity analysis in linear programs with trapezoidal fuzzy numbers, Journal of Intelligent and Fuzzy Systems27 (2014), 173–185.
28.
FengM., ManganJ., WongC., XuM. and LalwaniC., Investigating the different approaches to importance-performance analysis, The Service Industries Journal34 (2014), 1021–1041.
29.
GrzegorzewskiP. and MrówkaE., Trapezoidal approximations of fuzzy numbers, Fuzzy Sets and Systems153 (2005), 115–135.
30.
GustafssonA. and JohnsonM.D., Determining attribute importance in a service satisfaction model, Journal of Service Research7 (2004), 124–141.
31.
HairJ.F., AndersonR.E., TathamR.L. and BlackW.C., Multivariate Data Analysis,
Pretince-Hall, Upper Saddle River, New Jersey, 1995.
32.
HancockG.R. and KlockarsA.J., The effect of scale manipulations on validity: Targeting frequency rating scales for anticipated performance levels, Applied Ergonomics22 (1991), 147–154.
33.
HansenE. and BushR.J., Understanding customer quality requirements: Model and application, Industrial Marketing Management28 (1999), 119–130.
HeilpernS., The expected value of a fuzzy number, Fuzzy Sets and Systems47 (1992), 81–86.
36.
HsiehT.Y., LuS.T. and TzengG.H., Fuzzy MCDM approach for planning and design tenders selection in public office buildings, International Journal of Project Management22 (2004), 573–584.
37.
HuH-Y, LeeY-C, YenT-M and TsaiC-H, Using BPNN and DEMATEL to modify importance-performance analysis model-A study of the computer industry, Expert Systems with Applications36 (2009), 9969–9979.
38.
LaiI.K.W. and HitchcockM., Importance-performance analysis in tourism: A framework for researchers, Tourism Management48 (2015), 242–267.
39.
LiQ., A novel Likert scale based on fuzzy sets theory, Expert Systems with Applications40 (2013), 1609–1618.
40.
LiuS-T and KaoC., Fuzzy measures for correlation coefficient of fuzzy numbers, Fuzzy Sets and Systems128 (2002), 267–275.
41.
MatzlerK., SauerweinE. and HeischmidtK.A., Importanceperformance analysis revisited: The role of the factor structure of customer satisfaction, The Service Industries Journal23 (2003), 112–129.
42.
MountD.J. and SciariniM.P., IPA and DSI: Enhancing the usefulness of student evaluation of teaching data, Journal of Hospitality & Tourism Education10 (1999), 8–14.
43.
MountD.J., An empirical application of quantitative derived importance-performance analysis (QDIPA) for employee satisfaction, Journal of Quality Assurance in Hospitality & Tourism6 (2005), 65–76.
44.
NegoiţăC. and RalescuD., Application of Fuzzy Sets to System Analysis, Wiley, New York, 1975.
45.
NguyenH.T., (1978)A note on the extension principle for fuzzy sets, Journal of Mathematical Analysis and Applications64 , 369–380.
46.
RyanM.J., RaynerR. and MorrisonA., Diagnosing customer loyalty drivers: Partial least squares vs regression, Marketing Research11(Summer) (1999), 19–29.
47.
Shahsavari-PourN., Tavakkoli-MoghaddamR. and BasiriM-A, A new method for trapezoidal fuzzy numbers ranking based on the Shadow length and its application to manager’s risk taking, Journal of Intelligent and Fuzzy Systems26 (2014), 77–89.
48.
SnedecorG.W. and CochranW.G., Statistical MethodsIowa State University Press, Iowa, 1967.
49.
TianK.Y., An empirical study of factors that affect tourist satisfaction in scenic areas based on Fuzzy-IPA, Tourism Tribune25 (2010), 61–65.
50.
Usha MadhuriK., BabuS. Suresh and ShankarN. Ravi, Fuzzy risk analysis based on the novel fuzzy ranking with new arithmetic operations of linguistic fuzzy numbers, Journal of Intelligent and Fuzzy Systems26 (2014), 2391–2401.
51.
Van RyzinG.G., Importance-performance analysis of citizen satisfaction surveys, Public Administration85 (2007), 215–226.
52.
WanS-P and LiD-F, Possibility mean and variance based method for multi-attribute decision making with triangular intuitionsitic fuzzy numbers, Journal of Intelligent and Fuzzy Systems24 (2013), 743–754.
53.
WuW.Y., HsiaoS.W. and KuoH.P., Fuzzy set theory based decision model for determining market position and developing strategy for hospital service quality, Total Quality Management15 (2004), 439–456.
54.
YehC-H and KuoY-L, Evaluating passenger services of Asia-Pacific international airports, Transportation Research Part E39 (2003), 35–48.
55.
YehC-T, On improving trapezoidal and triangular approximations of fuzzy numbers, International Journal of Approximate Reasoning48 (2008), 297–313.
56.
YuC., Correlation of fuzzy numbers, Fuzzy Sets and Systems55 (1993), 303–307.
57.
YuS.C. and YuM.N., Fuzzy partial credit scaling: A valid approach for scoring the BECK depression inventory, Social Behavior and Personality: An International Journal35 (2007), 1163–1172.
58.
YuS.C. and YuB., Fuzzy item response model: A new approach to generate membership function to score psychological measurement, Quality and Quantity43 (2009), 381–390.
59.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
60.
ZadehL.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems1 (1978), 3–28.
