Generating Implications from One-Variable Functions

Abstract

In this paper, we firstly introduce two new classes of fuzzy implications generated from one-variable functions, called [Formula: see text]- and [Formula: see text]-implications, respectively. Then we give a series of necessary and sufficient conditions that these implications satisfy: left neutrality property, identity principle, ordering principle, law of contraposition, modus ponens and modus tollens, respectively. We also discuss the relations between [Formula: see text]- implication ([Formula: see text]-implications, respectively) and other known classes of fuzzy implications.