University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065411420140830Fuzzy Acts over Fuzzy Semigroups and Sheaves6173162410.22111/ijfs.2014.1624ENM.HaddadiDepartment of Mathematics, Statistics and Computer Sciences, Semnan
University, Semnan, IranJournal Article20111008lthough 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.<br /> 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.https://ijfs.usb.ac.ir/article_1624_7915f082437e766d5e60d3f04c95a162.pdf