MISO hierarchical inference engine satisfying the law of importation with aggregation functions

TL;DR

This paper develops three hierarchical fuzzy inference engines for MISO systems that satisfy the law of importation using specific aggregation functions, improving computational efficiency.

Contribution

It introduces a novel theoretical framework for constructing MISO fuzzy inference engines satisfying the law of importation with aggregation functions.

Findings

Identifies aggregation functions satisfying (LIA) for fuzzy implications

Characterizes fuzzy implications compatible with these aggregation functions

Constructs three hierarchical inference engines based on the theory

Abstract

Fuzzy inference engine, as one of the most important components of fuzzy systems, can obtain some meaningful outputs from fuzzy sets on input space and fuzzy rule base using fuzzy logic inference methods. In order to enhance the computational efficiency of fuzzy inference engine in multi-input-single-output(MISO) fuzzy systems,this paper aims mainly to investigate three MISO fuzzy hierarchial inference engines based on fuzzy implications satisfying the law of importation with aggregation functions (LIA). We firstly find some aggregation functions for well-known fuzzy implications such that they satisfy (LIA). For a given aggregation function, the fuzzy implication which satisfies (LIA) with this aggregation function is then characterized. Finally, we construct three fuzzy hierarchical inference engines in MISO fuzzy systems applying aforementioned theoretical developments.