Abstract
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.
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This research was supported by M. P. I. of Italy (60% and 40% 1986).
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Gerla, G. Decidability, partial decidability and sharpness relation for L-subsets. Stud Logica 46, 227–238 (1987). https://doi.org/10.1007/BF00372547
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DOI: https://doi.org/10.1007/BF00372547