Fuzzy Implications Generated by h-Generators

Abstract

In this work, by using h-generators, we introduce a new class of fuzzy implications, which are called (h, c)-generated implications. Some properties of (h, c)-implications are studied, including left neutrality, order property, exchange principle, law of contraposition, law of importation and distributivity over t-norms or t-conorms. We also discuss the intersections of both (h; c)-generated implications with R-, (S,N)-, QL-, f-, g- and h-implications and prove that (h, c)-generated implications are different from the ones above. In addition, we define (h, a, b, c)-implications by generalizing (h, c)-generated implications and obtain their properties similarly.