Fuzzy implication functions constructed from general overlap functions and fuzzy negations

TL;DR

This paper extends the construction of fuzzy implication functions by replacing t-norms with general overlap functions and fuzzy negations, broadening the theoretical framework and exploring their properties and relationships.

Contribution

It introduces a more general class of fuzzy implications using overlap functions, expanding previous models based on t-norms and negations.

Findings

New class of fuzzy implications derived from overlap functions

Characterization of properties and intersections with existing implications

Enhanced flexibility in fuzzy logic modeling

Abstract

Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative aggregation functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions. We also investigate their properties, characterization and intersections with other classes of fuzzy implication functions.