On the generalization of redundancy criteria for linguistic fuzzy rules

Abstract

The aim of this paper is to generalize existing criteria for determining redundant fuzzy linguistic rules, i.e., fuzzy IF-THEN rules that use evaluative linguistic expressions, and that can be freely omitted from a given rule-base without any impact Perception-based logical deduction (PbLD) is a specific inference method tailored to the linguistic fuzzy rules with linguistic expressions and it has been shown that this setting enables the investigation of redundant rules from a theoretical point of view. First of all, rules suspicious from redundancy are identified. Secondly, their elimination has to be checked as the suspicion can be canceled by a presence of a so-called canceling rule. However, the situation is complicated as even the impact of the canceling rule can be eliminated by another rule. The previous studies considered theoretical results and the final algorithm under the assumption of at most a single canceling rule.This paper generalizes the investigation to a more general case when even sets of rules that cancel a single suspicion can be found. We elaborate new criteria for such a purpose that enable to construct an algorithm for an automatic detection of redundant fuzzy linguistic rules. The elimination of redundant rules in a given system is an important step towards simplicity, clarity, and explainability, that moreover, decreases computational costs.