Klir-Yuan Fuzzy Implication in Fuzzy Relations

Abstract

Klir-Yuan fuzzy implication, as fuzzy implication generated from the standard strong fuzzy negation, the probabilistic sum t-conorm, and the product t-norm, represents a classical example of QL-implication, where QL-implications are the short for quantum logic fuzzy implications. In this paper we prove that the recent results on equivalences between fuzzy formulas and fuzzy dependencies remain invariant with respect to QL-implications when considered through Klir-Yuan fuzzy implication.