A sufficient condition on coherence of S-shaped radial implicative fuzzy systems

The paper addresses the issue of coherence of radial implicative fuzzy systems that use S-shaped fuzzy sets in antecedents of their rules. That means, in antecedents there are incorporated not only purely radial “bell shaped” fuzzy sets but also the S-shaped ones. We describe a computational model of these systems and introduce a sufficient condition that guarantees the existence of a consistent output for any possible input. In other words, we establish the condition assuring the rule base of a system to be non-contradictory for an arbitrary input.