A new class of fuzzy subsethood measures

Abstract

The idea of inclusion for fuzzy sets was firstly introduced by L. Zadeh in 1965 and since then many other studies proposed alternatives to indicate a degree to which a fuzzy set is included into another fuzzy set, called an inclusion degree or a subsethood measure. In this work we present a new class of fuzzy subsethood measures between fuzzy sets. We introduce a new definition of a fuzzy subsethood measure as an intersection of other axiomatizations by aggregating fuzzy implication operators. We also provide some construction methods to obtain these fuzzy subsethood measures. With our approach we recover some of the classical measures which have been discussed in the literature, as the one given by Goguen. We also show how we can use our developments to generate fuzzy entropies, fuzzy distances, penalty functions and similarity measures. Finally we study some fuzzy indexes generated from this new class of fuzzy subsethood measures.