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

In the previous years some authors have been elaborating on the measurementtheoretic 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. Key words: measurement theoretic axioms, fuzzy set theory, testing axioms

• Type: Journal
• Year: 2007
• Where: FSS
• Authors: C. Desimpelaere, Thierry Marchant
• Keywords: FSS 2007, Measurement Axioms, Pairwise Comparison Design, Social Science Data