Divergence measure between fuzzy sets using cardinality. (English) Zbl 1424.03032

Kobza, Vladimír

Kybernetika 53, No. 3, 418-436 (2017).

Summary: In this paper we extend the concept of measuring difference between two fuzzy subsets defined on a finite universe. The first main section is devoted to the local divergence measures. We propose a divergence measure based on the scalar cardinalities of fuzzy sets with respect to the basic axioms. In the next step we introduce the divergence based on the generating function and the appropriate distances. The other approach to the divergence measure is motivated by class of the rational similarity measures between fuzzy subsets expressed using some set operations (namely intersection, complement, difference and symmetric difference) and their scalar cardinalities. Finally, this concept is extended into the fuzzy cardinality in the last part. Some open problems omitted in this paper are discussed in the concluding remarks section.

MSC:

03E72

Theory of fuzzy sets, etc.

Keywords:

fuzzy set; divergence measure; scalar cardinality; fuzzy cardinality