Derived fuzzy importance of attributes based on the weakest triangular norm-based fuzzy arithmetic and applications to the hotel services

Document Type: Research Paper

Authors

1 Department of Mathematics and Informatics, University of Oradea, Universitatii 1, Oradea , Romania

2 Department of Economics, University of Oradea, Universitatii 1, Oradea , Romania

Abstract

The correlation between the performance of attributes and the overall
satisfaction such as they are perceived by the customers is often used to
calculate the importance of attributes in the crisp case. Recently, the method
was extended, based on the standard Zadeh extension principle, to the fuzzy
case, taking into account the specificity of the human thinking. The
difficulties of calculation are important and only approximations of the
analytic results can be obtained. In the present paper we give a simplified
and exact method to compute the derived importance of the attributes in the
case of input data given by triangular fuzzy numbers. The effective
calculation is based on the $T_{W}$-extension principle and it uses reasonable
computer resources even if a large number of attributes and customers is
considered. The proposed derived method is later on compared with other
methods of calculation of the fuzzy importance of attributes. The results of
a survey with respect to the quality of hotel services in Oradea (Romania)
are subject to the application of the proposed method.

Keywords


[1] J. Abalo, J. Varela and V. Manzano, Importance values for importance-performance analysis:
A formula for spreading out values derived from preference rankings, Journal of Bussiness
Research, 60 (2007), 115{121.
[2] D. R. Bacon, A comparison of approaches to Importance-Performance Analysis, International
Journal of Marketing Research, 45 (2003), 55{71.
[3] A. I. Ban and L. Coroianu, Simplifying the search for e ective ranking of fuzzy numbers,
IEEE Transactions on Fuzzy Systems, 23 (2014), 327{339.
[4] A. I. Ban, O. I. Ban and D. A. Tuse, Calculation of the fuzzy importance of attributes based
on the correlation coecient, applied to the quality of hotel services, Journal of Intelligent
and Fuzzy Systems, 30 (2015), 583{596.
[5] A. Ban and O. Ban, Optimization and extensions of a fuzzy multicriteria decision making
method and applications to selection of touristic destinations, Expert Systems with Applica-
tions, 39 (2012), 7216{7225.
[6] A. I. Ban and L. Coroianu, Characterization of the ranking indices of triangular fuzzy num-
bers. In: A. Laurent, O. Strauss, B. Bouchon-Meunier and R.R. Yager (Eds.), Communi-
cations in Computer and Information Science, vol. 443, Springer-Verlag, Berlin, Heidelberg,
2014, pp. 254{263.
[7] O. Ban, Fuzzy multicriteria decision making method applied to selection of the best touristic
destinations, International Journal of Mathematical Models and Methods in Applied Science,
5 (2011), 264{271.
[8] O. I. Ban and I. T. Mester, Using Kano two dimensional service quality classi cation and
characteristic analysis from the perspective of hotels' clients of Oradea, Journal of Tourism-
Studies and Research in Tourism, 18 (2014), 30{36.
[9] S. Chanas, On the interval approximation of a fuzzy number, Fuzzy Sets and Systems, 122
(2001), 353{356.
[10] P. T. Chang, P. F. Pai, K. P. Lin and M. S. Wu, Applying fuzzy arithmetic to the system
dynamics for the customer-producer-employment model, International Journal of Systems
Science, 37 (2006), 673{698.
[11] T. C. Chu and Y. Lin, An extension to fuzzy MCDM, Computers and Mathematics with
Applications, 57 (2009), 445{454.
[12] W. Deng, Using a revised importance-performance analysis approach: The case of Taiwanese
hot springs tourism, Tourism Management, 28 (2007), 1274{1284.
[13] W. J. Deng and W. Pei, Fuzzy neural based importance-performance analysis for determining
critical service attributes, Expert Systems with Applications, 36 (2009), 3774{3784.
[14] W. J. Deng, Fuzzy importance-performance analysis for determining critical service at-
tributes, International Journal of Service Industry Management, 19 (2008), 252{270.

[15] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets. theory and applications, World
Scienti c, Singapore, 1994.
[16] D. Dubois and H. Prade, Operations on fuzzy numbers, International Journal of Systems
Sciences, 9 (1978), 613{626.
[17] D. Dubois and H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24
(1987), 279{300.
[18] M. Feng, J. Mangan, C. Wong, M. Xu and C. Lalwani, Investigating the di erent approaches
to importance-performance analysis, The Service Industries Journal, 34 (2014), 1021{1041.
[19] J. F. Hair, R. E. Anderson, R. L. Tatham and W. C. Black, Multivariate data analysis,
Pretince-Hall, Upper Saddle River, New Jersey, 1995.
[20] T. Hajjari, Fuzzy risk analysis based on ranking of fuzzy numbers via new magnitude method,
Iranian Journal of Fuzzy Systems, 12 (2015), 17-29.
[21] G. R. Hancock and A. J. Klockars, The e ect of scale manipulations on validity: Targeting
frequency rating scales for anticipated performance levels, Applied Ergonomics, 22 (1991),
147-154.
[22] D. H. Hong, Fuzzy measures for a correlation coecient of fuzzy numbers under TW (the
weakest t-norm)-based fuzzy arithmetic operations, Information Sciences, 176 (2006), 150-
160.
[23] D. H. Hong, Shape preserving multiplications of fuzzy intervals, Fuzzy Sets and Systems, 123
(2001), 81-84.
[24] D. H. Hong, On shape-preserving additions of fuzzy intervals, Journal of Mathematical Anal-
ysis and Applications, 267 (2002), 369{376.
[25] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Springer, Dordrecht, 2000.
[26] A. Kolesarova, Additive preserving the linearity of fuzzy interval, Tatra Montains Mathemat-
ical Publications, 6 (1994), 75{81.
[27] M. Kumar, Applying weakest t-norm based approximate intuitionistic fuzzy arithmetic oper-
ations on di erent types of intuitionistic fuzzy numbers to evaluate reliability of PCBA fault,
Applied Soft Computing, 23 (2014), 387{406.
[28] Q. Li, A novel Likert scale based on fuzzy sets theory, Expert Systems with Applications, 40
(2013), 1609-1618.
[29] K. P. Lin, M. J. Wu, K. C. Hung and Y. Kuo, Developing a Tw (the weakest t-norm) fuzzy
GERT for evaluating uncertain process reliability in semiconductor manufacturing, Applied
Soft Computing, 11 (2011), 5165-5180.
[30] K. P. Lin, W. Wen, C. C. Chou, C. H. Jen and K. C. Hung, Applying fuzzy GERT with
approximate fuzzy arithmetic based on the weakest t-norm operations to evaluate repairable
reliability, Applied Mathematical Modelling, 35 (2011), 5314-5325.
[31] S. T. Liu and C. Kao, Fuzzy measures for correlation coecient of fuzzy numbers, Fuzzy Sets
and Systems, 128 (2002), 267-275.
[32] K. Matzler, E. Sauerwein and K. A. Heischmidt, Importance-performance analysis revisited:
the role of the factor structure of customer satisfaction, The Service Industries Journal, 23
(2003), 112-129.
[33] R. Mesiar, Shape preserving additions of fuzzy interval, Fuzzy Sets and Systems, 86 (1997),
73-78.
[34] D. J. Mount and M. P. Sciarini, IPA and DSI: Enhancing the usefulness of student evaluation
of teaching data, Journal of Hospitality & Tourism Education, 10 (1999), 8-14.
[35] D. J. Mount, An empirical application of quantitative derived importance-performance anal-
ysis (QDIPA) for employee satisfaction, Journal of Quality Assurance in Hospitality &
Tourism, 6 (2005), 65-76.
[36] W. Pedrycz, Why triangular membership functions?, Fuzzy Sets and Systems, 64 (1994),
21-30.
[37] S. Sharma, Applied Multivariate Techniques, John Wiley & Sons, Singapore, 1996.
[38] G. W. Snedecor and W. G. Cochran, Statistical Methods, Iowa State University Press, Iowa,
1967.

[39] S. Wan, J. Dong and D. Yang, Trapezoidal intuitionistic fuzzy prioritized aggregation oper-
ators and application to multi-attribute decision making, Iranian Journal of Fuzzy Systems,
12(4) (2015), 1-32.
[40] C. H. Yeh and Y. L. Kuo, Evaluating passenger services of Asia-Paci c international airports,
Transportation Research Part E, 39 (2003), 35-48.
[41] S. C. Yu and M. N. Yu, Fuzzy partial credit scaling: a valid approach for scoring the BECK
depression inventory, Social Behavior and Personality: An International Journal, 35 (2007),
1163-1172.
[42] S. C. Yu and B. Yu, Fuzzy item response model: a new approach to generate membership
function to score psychological measurement, Quality and Quantity, 43 (2009), 381-390.
[43] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353.
[44] L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1 (1978),
3-28.