Fuzzy Acts over Fuzzy Semigroups and Sheaves

Document Type : Research Paper


Department of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran


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.


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