Measures of Fuzziness under Different Uses of Fuzzy Sets

Abstract. In this paper we discuss on the relationship between fuzziness and its measuring on the one side, and the possible uses of fuzzy sets on the other side. We conclude that the usual axioms and measures of fuzziness disregard the commensurability assumption and view the fuzzy set as a collection of fuzzy singletons. We propose new axioms and a relation “less fuzzy than ” for a conjunctive view of fuzzy sets under the commensurability assumption. We show that a measure of fuzziness previously introduced by the authors comply with our proposal.