Approximate reasoning with aggregation functions satisfying GMP rules

TL;DR

This paper develops three new approximate reasoning schemes using aggregation functions that satisfy GMP rules, enhancing fuzzy inference methods like FMP and FMT.

Contribution

It introduces three novel approximate reasoning schemes with aggregation functions satisfying GMP rules, extending existing fuzzy inference frameworks.

Findings

The properties of fuzzy implications generated by aggregation functions are characterized.

An A-compositional rule of inference (ACRI) is proposed as an extension of Zadeh's CRI.

The validity of the proposed reasoning schemes is confirmed under GMP rules.

Abstract

To strengthen the effectiveness of approximate reasoning in fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) problems, three approximate reasoning schemes with aggregation functions are developed and their validity is respectively investigated in this paper. We firstly study some properties of fuzzy implication generated by aggregation function. And then present an $A$-compositional rule of inference (ACRI) as an extension of Zadeh's CRI replacing $t$-norm by an aggregation function. The similarity-based approximate reasoning with aggregation functions is further discussed. Moreover, we provide the quintuple implication principle (QIP) method with aggregation functions to solve FMP and FMT problems. Finally, the validity of our proposed three approximate reasoning approaches is respectively analyzed using GMP rules in detail.