Inferential confidence intervals for fuzzy analysis of teaching satisfaction Donata Marasini 1 • Piero Quatto 1 • Enrico Ripamonti 1 Ó Springer Science+Business Media Dordrecht 2016 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 mem- bership values. Second, inferential confidence intervals (ICI), calculated through Boot- strap-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. Keywords Fuzzy sets  Intuitionistic fuzzy sets  Teaching evaluation  Bootstrap methods  Inferential confidence intervals  Satisfaction indices  Positive false discovery rate 1 Introduction 1.1 Evaluating university courses In this paper we consider a latent construct, satisfaction of University students, and we put forward a general method to quantifying questionnaire ratings. This method combines the & Enrico Ripamonti enrico.ripamonti@unimib.it 1 Department of Economics, Management and Statistics, Statistical Section, Universita ` degli Studi di Milano-Bicocca, Piazza Ateneo Nuovo 1, 20126 Milan, Italy 123 Qual Quant DOI 10.1007/s11135-016-0349-7