Hierarchical similarity-based approximate reasoning with restricted equivalence function

TL;DR

This paper introduces hierarchical similarity-based approximate reasoning methods utilizing restricted equivalence functions to improve inference efficiency and control rule explosion in fuzzy systems.

Contribution

It characterizes REFs with aggregation functions and proposes two hierarchical SBAR methods based on REFs to enhance reasoning and reduce fuzzy rule explosion.

Findings

REFs can effectively measure fuzzy set similarity.

Hierarchical SBAR methods improve inference efficiency.

Proposed methods restrain fuzzy rule explosion.

Abstract

Given that the restricted equivalence functions (REFs) can serve to measure the similarity of two fuzzy sets, this motivates the integration of REFs with similarity-based approximate reasoning systems to enhance inference capabilities. Therefore, this work primarily constructs hierarchical similarity-based approximate reasoning (SBAR) using REFs. Specifically, we first characterize REFs with a given aggregation function, then discuss the approximation equality of SBAR method proposed by Raha et al. with REFs. Finally, we suggest two REF-based hierarchical Raha's SBAR methods which efficiently restrain the explosion of fuzzy rules.