Coherence of Radial Implicative Fuzzy Systems

Abstract

In the paper we address the problem of coherence of a special class of fuzzy systems -the class of so called radial implicative fuzzy systems. A fuzzy system Is coherent if for an arbitrary input there is guaranteed that a non-empty appropriate output exists, which corresponds to the statement that there are no contradictory rules in the system's rule base. For conjunctive fuzzy systems coherence is generally always satisfied. However, for implicative fuzzy systems this is not automatically the case. In the paper we specify sufficient conditions for coherence of radial implicative fuzzy systems. Radial fuzzy systems are systems exhibiting the radial property which simplifies their computational scheme and enables efficiently answer questions on their important properties.