Fuzzy Approximate Reasoning Method based on Least Common Multiple and its Property Analysis

TL;DR

This paper introduces a novel fuzzy approximate reasoning method based on least common multiple (LCM), improving reasoning accuracy, information retention, and control in fuzzy systems through theoretical and experimental validation.

Contribution

The paper proposes a new LCM-based fuzzy reasoning method and analyzes its properties, demonstrating improvements over existing methods in reasoning reductiveness and control.

Findings

Enhanced reductive property in fuzzy reasoning

Reduced information loss during reasoning

Improved controllability in fuzzy control systems

Abstract

This paper shows a novel fuzzy approximate reasoning method based on the least common multiple (LCM). Its fundamental idea is to obtain a new fuzzy reasoning result by the extended distance measure based on LCM between the antecedent fuzzy set and the consequent one in discrete SISO fuzzy system. The proposed method is called LCM one. And then this paper analyzes its some properties, i.e., the reductive property, information loss occurred in reasoning process, and the convergence of fuzzy control. Theoretical and experimental research results highlight that proposed method meaningfully improve the reductive property and information loss and controllability than the previous fuzzy reasoning methods.