Further results on fuzzy negations and implications induced by fuzzy conjunctions and disjunctions

TL;DR

This paper investigates properties of fuzzy negations derived from conjunctions and disjunctions, and explores implications generated from these negations, providing new characterizations and descriptions within fuzzy logic.

Contribution

It offers new characterizations of fuzzy negations induced by conjunctions and disjunctions, and describes implications generated from these negations, advancing fuzzy logic theory.

Findings

Characterization of fuzzy negations from conjunctions and disjunctions

Descriptions of $(D,N)$-implications generated from fuzzy negations

Analysis of continuous $(D,N)$-implications in fuzzy logic

Abstract

In this article, we deeply investigate some properties of fuzzy negations induced from fuzzy conjunctions (resp. disjunctions), which are then applied to characterizing the fuzzy negations. We further use the obtained characterization of fuzzy negations to explore some properties of $(D,N)$-implications generated from fuzzy disjunctions and negations. We finally describe $(D,N)$-implications (resp. continuous $(D,N)$-implications) generated from fuzzy disjunctions and negations.