FUZZY M-ACTS OVER A SEMIGROUP: EXTENSION PRINCIPLE

Although the very well established and favorite theories of Fuzzy Sets and Sheaves have been developed and studied independently, Ulrich H¨ohle 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 H¨ohle’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, we study the fuzzy version of the important, very useful, and favorite structure of acts over a fuzzy semigroup, so to say, with its internal as well as external definitions. Moreover extension principle, which enables us to extend every (universal) algebraic operation on an algebra A to an operation on the fuzzy subsets of A, is one of the most important tools in fuzzy set theory and fuzzy algebras. So we study the extension principle for the categoryof fuzzy S-acts

کلیدواژه ها:

fuzzy algebra ، fuzzy act ، sheaf