TL;DR
Radial fuzzy systems utilize radial functions for membership, maintaining shape properties that make their computational models mathematically tractable, with discussions on coherence conditions for implicative variants.
Contribution
This paper introduces the class of radial fuzzy systems, highlighting their shape-preserving properties and mathematical tractability, along with coherence analysis.
Findings
Radial property ensures shape preservation in fuzzy rules.
Radial fuzzy systems are mathematically tractable.
A sufficient condition for coherence is provided.
Abstract
The class of radial fuzzy systems is introduced. The fuzzy systems in this class use radial functions to implement membership functions of fuzzy sets and exhibit a shape preservation property in antecedents of their rules. The property is called the radial property. It enables the radial fuzzy systems to have their computational model mathematically tractable under both conjunctive and implicative representations of their rule bases. Coherence of radial implicative fuzzy systems is discussed and a sufficient condition for coherence is stated.
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