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SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 6، شماره 4، اسفند 2009، صفحه 73-87 اصل مقاله (294.65 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2009.542 | ||
| نویسندگان | ||
| Mahmood Bakhshi1؛ Rajab Ali Borzooei* 2 | ||
| 1Department of Mathematics, University of Bojnord, Bojnord, Iran | ||
| 2Department of Mathematics, Shahid Beheshti University, Tehran, Iran | ||
| چکیده | ||
| In this paper, we deal with Molaei’s generalized groups. We define the notion of a fuzzy generalized subgroup with respect to a t-norm (or T-fuzzy generalized subgroup) and give some related properties. Especially, we state and prove the Representation Theorem for these fuzzy generalized subgroups. Next, using the concept of continuity of t-norms we obtain a correspondence between TF(G), the set of all T-fuzzy generalized subgroups of a generalized group G, and the set of all T-fuzzy generalized subgroups of the corresponding quotient generalized group. Subsequently, we study the quotient structure of T-fuzzy generalized subgroups: we define the notion of a T-fuzzy normal generalized subgroup, give some related properties, construct the quotient generalized group, state and prove the homomorphism theorem. Finally, we study the lattice of T-fuzzy generalized subgroups and prove that TF(G) is a Heyting algebra. | ||
| کلیدواژه‌ها | ||
| Generalized groups؛ Fuzzy generalized subgroups؛ t-norm؛ Heyting algebra | ||
| مراجع | ||
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