An empirical test of some measurement-theoretic axioms for fuzzy sets

Authors:
C. Desimpelaere;T. Marchant
Affiliations:
Department of Data-Analysis, Faculty of Psychology and Educational Sciences, Ghent University, H. Dunantlaan 1, 9000 Ghent, Belgium;Department of Data-Analysis, Faculty of Psychology and Educational Sciences, Ghent University, H. Dunantlaan 1, 9000 Ghent, Belgium
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

In the previous years some authors have been elaborating on the measurement-theoretic foundations of fuzzy set theory. A well-known problem in this approach is the difficult applicability of the deterministically formulated axioms on data obtained from an expert (or social science data in general). In this paper a statistical method is proposed which can be used for the testing of measurement axioms in a pairwise comparison design. Consequently we apply this method for the testing of two of these axioms (i.e. Transitivity and Order of Operations) used in the context of fuzzy set theory. The results clearly indicate that subjects act in agreement with Transitivity, but, for Order of Operations there is no such vivid evidence, which may have repercussions for some of the earlier theoretical work.