We propose the notion of partial recursiveness and strong partial recursiveness for fuzzy maps. We prove that a fuzzy map f is partial recursive if and only if it is computable by a Turing fuzzy machine and that f is strongly partial recursive and deterministic if and only if it is computable via a deterministic Turing fuzzy machine. This gives a simple and manageable tool to investigate about the properties of the fuzzy machines.

If X is set and L a lattice, then an L-subset or fuzzy subset of X is any map from X to L, [11]. In this paper we extend some notions of recursivity theory to fuzzy set theory, in particular we define and examine the concept of almost decidability for L-subsets. Moreover, we examine the relationship between imprecision and decidability. Namely, we prove that there exist infinitely indeterminate L-subsets with no more precise decidable versions and classical subsets whose unique shaded (...) decidable versions are the L-subsets almost-everywhere indeterminate. (shrink)