Abstract
Although fuzzy set theory and sheaf theory have been developed and studied independently, Ulrich Hohle shows that a large part of fuzzy set theory is in fact a subeld of sheaf theory. Many authors have studied math- ematical structures, in particular, algebraic structures, in both categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra A, the set of fuzzy algebras over A and the set of subalgebras of the constant sheaf of algebras over A are order isomorphic. Then, among other things, we study the category of fuzzy acts over a fuzzy semigroup, so to say, with its universal algebraic as well as classic algebraic denitions.
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