The Measure of Fuzzy Filters on BL-Algebras

Abstract

The new concept of the fuzzy filter degree was given by means of the implication operator, which enables to measure a degree to which a fuzzy subset of a BL-algebra is a fuzzy filter. In this paper, we put forward several equivalent characterizations of the fuzzy filter degree by studying its properties and the relationship with level cut sets. Furthermore, we study the fuzzy filter degrees of the intersection and fuzzy direct products of fuzzy subsets and investigate the fuzzy filter degrees of the image and the preimage of a fuzzy subset under a homomorphism.