Decidability,partial decidability and sharpness relation for L-subsets

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.This research was supported by M. P. I. of Italy (60% and 40% 1986).