Coherence of radial implicative fuzzy systems with nominal consequents

Abstract

In the paper we are interested in the question of coherence of radial implicative fuzzy systems with nominal consequents (radial I-FSs with NCs). Implicative fuzzy systems are fuzzy systems employing residuated fuzzy implications for representation of IF-THEN structure of their rules. Radial fuzzy systems are fuzzy systems exhibiting the radial property in antecedents of their rules. The property simplifies computational model of radial systems and makes the investigation of their properties more tractable. A fuzzy system has nominal consequents if its output is defined on a finite unordered set of possible actions which are generally quantitatively incomparable. The question of coherence is the question of under which conditions we are assured that regardless the input to the system is, an output of the system exists, i.e., the output is non-empty. In other words, a fuzzy system is coherent if it has no contradictory rules in its rule base. In the paper we state sufficient conditions for a radial I-FS with NCs to be coherent