fuzzy acts over fuzzy semigroups and sheaves

lthough 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 subfield of sheaf theory. many authors have studied mathematical 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 definitions.