Representability of a fuzzy predicate from a category with fuzzy subsets

Abstract

The failure of existence of products in a non-trivial category with fuzzy subsets raises the problem of how to talk about predicates and their representability. The concept of predicate is set off in an arbitrary category in order to examine the situation in a category with fuzzy subsets. The representability of the general concept of predicate is problematic. Two restrictions of this are natural extensions of the ordinary concept. The first, which we term fuzzy predicates shows the multivariant nature of fuzziness. The second, a restriction, is exactly the concept of predicate introduced by Zadeh. Furthermore ordinary products are representative of Zadeh predicates.