Abstract
Fuzzy sets are an extension of classical sets, used to mathematically model indefinite concepts, such as that of customer satisfaction. This is obtained by introducing a membership function expressing the degree of membership of the elements to a set. Intuitionistic fuzzy sets represent an extension of the theory of fuzzy sets, in which also a suitable non-membership function is defined. In this paper we aim at quantifying a latent construct, namely satisfaction, using fuzzy sets and intuitionistic fuzzy sets. We put forth a general evaluation method: first, we introduce a fuzzy satisfaction index to obtain membership values. Second, inferential confidence intervals (ICI), calculated through Bootstrap-t and percentile procedures, are used to assess the uncertainty underpinning membership and non-membership estimates. Third, we address the problem of optimal and multiple ICI, as well as their generalization through p values and q-values. In particular, we consider the problem of analyzing the responses to evaluation questionnaires. We apply this new method to a national program of evaluation of University courses and we discuss our framework in comparison with other evaluation techniques.
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Notes
In Italy, the evaluation of University courses became a compulsory requirement activity for all Universities, starting from 2000; Law 370, 19th October, 1999, see http://www.anvur.org/.
In our dataset, bootstrap-t and percentile, when applied to calculate ICI for proportions, provided very similar results. For this reason, in the application we’ll only show the results relative to the percentile procedure.
References
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Atanassov, K.T.: On intuitionistic Fuzzy Sets Theory. Springer, New York (2012)
Bede, B.: Mathematics of Fuzzy Sets and Fuzzy Logic. Springer, Heidelberg (2013)
Bergen Communiqué 2005: Bergen Communiqué: The European higher education area—achieving the goals. In: Communiqué of the Conference of European Ministers Responsible for Higher Education, Bergen (2005). 19–20 May 2005
Bilgiç, T., Türkşen, I.B.: Measurement of membership functions: theoretical and empirical work. In: Dubois, D., Prade, H.M., Prade, H. (eds.) Fundamentals of Fuzzy Sets, pp. 195–227. Springer, New York (2000)
Bucarest Communiqué: Bucarest communiqué 2012: Making the most of our potential: Consolidating the European higher education area. In: Communiqué of the Conference of European Ministers Responsible for Higher Education, Bucarest (2012). 26–27 Apr 2012
Cerioli, A., Zani, S.: A fuzzy approach to the measurement of poverty. In: Dagum, C., Zenga, M. (eds.) Income and wealth distribution, inequality and poverty, Studies in contemporary Economics, pp. 272–284. Springer Verlag, Berlin (1990)
Cumming, G., Finch, S.: Inference by eye: confidence intervals and how to read pictures of data. Am. Psychol. 60, 170–180 (2005)
D’Elia, A., Piccolo, D.: A mixture model for preference data analysis. Comput. Stat. Data Anal. 49, 917–934 (2005)
de Jager, J., Gbadamosi, G.: Specific remedy for specific problem: measuring service quality in South African higher education. High. Educ. 60, 251–267 (2010)
ENQA: European Association for Quality Assurance in Higher Education 2009. Standards and Guidelines for Quality Assurance in the European Higher Education Area, 3rd edn. Helsinki (2009)
Giles, R.: The concept of grade of membership. Fuzzy Sets Syst. 25, 297–323 (1988)
Goldstein, H., Healy, M.J.: The graphical presentation of a collection of means. J. R. Stat. Soc. Ser. A 158, 175–177 (1995)
Good, P.I.: Permutation, parametric and bootstrap tests of hypotheses. Springer, New York (2005)
Iannario, M., Piccolo, D.: CUB models: statistical methods: and empirical evidence. In: Kenett, R.S., Salini, S. (eds.) Modern Analysis of Customer Surveys: with applications using R, pp. 231–258. Wiley, New York (2012)
Kosko, B.: Fuzzy Thinking: The New Science of Fuzzy Logic. Hyperion, New York (1993)
Marasini, D., Quatto, P.: A characterization of linear satisfaction measures. Metron 72, 17–23 (2014)
Marasini, D., Quatto, P., Ripamonti, E.: Intuitionistic fuzzy sets in questionnaire analysis. Qual. Quant. 50, 767–790 (2016)
Pitts, A.M.: Fuzzy sets do not form a topos. Fuzzy Sets Syst. 8, 101–104 (1982)
Salini, S., Kenett, R.: Bayesian networks of customer satisfaction survey data. J. Appl. Stat. 11, 1177–1189 (2009)
Shao, J., Tu, D.: The Jackknife and Bootstrap. Springer, New York (1995)
Smithson, M., Verlukien, J.: Fuzzy Set Theory: Applications in the Social Sciences. Sage, London (2006)
Storey, J.D.: A direct approach to false discovery rates. J. R. Stat. Soc. Ser. B Stat. Methodol. 64, 479–498 (2002)
Tryon, W.W.: Evaluating statistical difference, equivalence, and indeterminacy using inferential confidence intervals: an integrated alternative method of conducting null hypothesis statistical tests. Psychol Methods 6, 371–386 (2001)
Tryon, W.W., Lewis, C.: Evaluating independent proportions for statistical difference, equivalence, indeterminacy, and trivial difference using inferential confidence intervals. J. Educ. Behav. Stat. 34, 171–189 (2009)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zani, S., Milioli, M.A., Morlini, I.: Fuzzy methods and satisfaction indices. In: Kenett, R.S., Salini, S. (eds.) Modern Analysis of Customer Surveys: With Applications Using R, pp. 439–456. Wiley, New York (2012)
Zimmermann, H.J.: Fuzzy set theory. Wiley Interdiscip. Rev. Comput. Stat. 2, 317–332 (2010)
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Marasini, D., Quatto, P. & Ripamonti, E. Inferential confidence intervals for fuzzy analysis of teaching satisfaction. Qual Quant 51, 1513–1529 (2017). https://doi.org/10.1007/s11135-016-0349-7
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DOI: https://doi.org/10.1007/s11135-016-0349-7