Associativeness versus recursiveness

Abstract

Fuzzy connectives used to be assumed associative. In this way, key operational difficulties are solved by means of a single binary operator. In this paper we point out that the main property in order to assure operativeness should be recursiveness, which is weaker than associativity. If calculus can be obtained by means of a recursive application of a sequence of binary connectives, we still can develop operative models. It is then clearly seen that a fuzzy role should be always understood as a family of fuzzy connectives. Associativity will appear when a fuzzy rule can be characterized by a single binary connective. Associativity assumption is therefore excluding from our model key rules in practice.