Introduction to the concept of recursiveness of fuzzy functions (Q1100197)

The hypothesis that the class of recursive functions is identical with the one of functions being computable by a Turing machine is known as ``Church's soft hypothesis''. The main purpose of this article is to extend this hypothesis to the fuzzy calculus. Let \(W=([0,1],\oplus,\otimes,\leq)\) be an ordered semiring. The fuzzy functions are considered as associating an output to an input with membership degree belonging to W. For such W-functions the concepts of computability and recursiveness are extended, obtaining the so-called W- computability and W-recursiveness, respectively. Some properties of W- recursive functions are analyzed and the equivalence between W-recursive and W-computable functions is shown.