MP and MT properties of fuzzy inference with aggregation function

TL;DR

This paper investigates the properties of fuzzy inference models, specifically fuzzy modus ponens and tollens, using aggregation functions, and demonstrates their generality and effectiveness through theoretical analysis and examples.

Contribution

It introduces and analyzes the A-compositional rule of inference (ACRI) based on aggregation functions, extending traditional fuzzy inference methods with broader applicability.

Findings

Aggregation functions provide more generality than t-norms, uninorms, and overlap functions.

ACRI method effectively handles FMP and FMT problems with demonstrated theoretical properties.

Examples illustrate the closeness of output to expected values when inputs are near certain conditions.

Abstract

As the two basic fuzzy inference models, fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) have the important application in artificial intelligence. In order to solve FMP and FMT problems, Zadeh proposed a compositional rule of inference (CRI) method. This paper aims mainly to investigate the validity of A-compositional rule of inference (ACRI) method, as a generalized CRI method based on aggregation functions, from a logical view and an interpolative view, respectively. Specifically, the modus ponens (MP) and modus tollens (MT) properties of ACRI method are discussed in detail. It is shown that the aggregation functions to implement FMP and FMT problems provide more generality than the t-norms, uninorms and overlap functions as well-known the laws of T-conditionality, U-conditionality and O-conditionality, respectively. Moreover, two examples are also given to illustrate our theoretical results. Especially, Example 6.2 shows that the output B' in FMP(FMT) problem is close to B(DC) with our proposed inference method when the fuzzy input and the antecedent of fuzzy rule are near (the fuzzy input near with the negation of the seccedent in fuzzy rule).