Elsevier

Fuzzy Sets and Systems

Volume 158, Issue 12, 16 June 2007, Pages 1348-1359
Fuzzy Sets and Systems

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

https://doi.org/10.1016/j.fss.2007.02.011Get rights and content

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.

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