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21

Fuzzy Methods and Satisfaction Indices

Sergio Zani, Maria Adele Milioli and Isabella Morlini

This chapter develops a framework that uses fuzzy set theory in order to measure customer satisfaction, starting from a survey with several questions. The basic concepts of the theory of the fuzzy numbers are briefly described. A criterion based on the sampling cumulative function, which assigns values to the membership function with reference to each quantitative, ordinal and binary variable, is suggested. Weighting and aggregation operators for the variables are considered. An application to ABC 2010 annual customer satisfaction survey data shows the usefulness of the fuzzy set approach: the gradual transition from very dissatisfied to really satisfied customers is captured by fuzzy composite indices. The comparison with the classical methods for the measurement of customer satisfaction highlights the advantages of the suggested criterion from both the theoretical and operational points of view.

21.1 Introduction

Fuzzy set theory was introduced by Zadeh (1965), and Zadeh describes it in the foreword to Zimmermann (2001) as basically ‘a theory in which everything is a matter of degree or, to put it figuratively, everything has elasticity’.

In classical (crisp) set theory, an element either belongs to a set, or not, and in conventional dual logic, a statement can either be true or false. By contrast, in fuzzy set theory, an element presents a membership function value to a fuzzy set ...

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