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Fuzzy Acts over Fuzzy Semigroups and Sheaves | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 11، شماره 4، آبان 2014، صفحه 61-73 اصل مقاله (334.22 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1624 | ||
| نویسنده | ||
| M. Haddadi* | ||
| Department of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| fuzzy algebra؛ fuzzy act؛ sheaf | ||
| مراجع | ||
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