Hierarchical similarity-based approximate reasoning with restricted equivalence function
General Mathematics
2026-05-04 v1
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.
Cite
@article{arxiv.2605.00048,
title = {Hierarchical similarity-based approximate reasoning with restricted equivalence function},
author = {Dechao Li and Yuhui Zhu},
journal= {arXiv preprint arXiv:2605.00048},
year = {2026}
}