ON MEASURES OF FUZZINESS AND FUZZY COMPLEMENTS

Abstract

An axiomatic framework for formalizing the most general class of fuzzy complements is introduced in this paper. It is then used for investigating a general class of measures of fuzziness based on the view that the degree of fuzziness of a fuzzy set should characterize the lack of distinction between the set and its complement. It is shown that the various measures of fuzziness described previously in the literature are special cases of this general class. A class of so-called distance-based measures of fuzziness is also introduced. These measures are described in terms of the notion of an aggregation function of differences between the membership grades characterizing a fuzzy set and those of its complement. It is shown that the class of distance-based measures is equal to the class of general measures of fuzziness. It is also shown that, given a particular fuzzy complement, aggregation functions which differ only in a multiplication constant represent the same measure of fuzziness.