Characterization of fuzzy implication functions with a continuous α-natural negation satisfying the law of importation with a given uninorm-revisited

Abstract

In this work, we partially study a problem which generalizes and comes from an open problem related to law of importation and suggested by international conference on fuzzy set theory and applications 8th in 2006. In fact, this problem has also partially been investigated in [16]. The obtained results in our paper dramatically extend the aforementioned ones. In detail, we characterizes all fuzzy implications with a continuous α-natural negation which satisfy the law of importation w.r.t a fixed uninorm U, where U is a uninorm continuous in (0,1)2.