Relevance of classes in a fuzzy partition. A study from a group of aggregation operators

Abstract

This paper presents a study of the relevance property in a fuzzy partition from a fuzzy classification system. This study allows establishing a stopping criterion for the inclusion of a class in a fuzzy partition based on relevance. Such a criterion is constructed from a stable relationship on the commutative group formed by two new mappings (and the aggregation operators conjunctive and disjunctive) of the fuzzy classification system. The criterion is illustrated through an example on image analysis by the fuzzy c-means algorithm.