($S$,$N$,$T$)-Implications

TL;DR

This paper introduces a new class of fuzzy implications called ($S$,$N$,$T$)-implications, inspired by logical equivalences, and explores their properties and methods to derive related t-norms, t-conorms, and negations.

Contribution

The paper defines ($S$,$N$,$T$)-implications and studies their properties, providing methods to obtain related fuzzy operators from them.

Findings

Characterization of ($S$,$N$,$T$)-implications

Methods to derive t-norms and t-conorms from these implications

Analysis of properties that define this new class

Abstract

In this paper we introduce a new class of fuzzy implications called ($S$,$N$,$T$)-implications inspired in the logical equivalence $p\rightarrow q \equiv \neg(p\wedge\neg q)\vee\neg p$ and present a brief study of some of the main properties that characterize this class. We present methods of obtaining $t$-norms and $t$-conorms from an ($S$,$N$,$T$)-implication and a fuzzy negation.