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Iranian Journal of Fuzzy Systems، جلد ۶، شماره ۴، صفحات ۷۳-۸۷
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عنوان فارسی |
SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS |
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چکیده فارسی مقاله |
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. |
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کلیدواژههای فارسی مقاله |
Generalized groups، Fuzzy generalized subgroups، t-norm، Heyting
algebra، |
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عنوان انگلیسی |
SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS |
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چکیده انگلیسی مقاله |
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. |
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کلیدواژههای انگلیسی مقاله |
Generalized groups, Fuzzy generalized subgroups, t-norm, Heyting
algebra |
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نویسندگان مقاله |
محمود بخشی | department of mathematics, university of bojnord, bojnord, iran سازمان اصلی تایید شده: دانشگاه بجنورد (University of bojnord)
رجبعلی برزویی | rajab ali department of mathematics, shahid beheshti university, tehran, iran سازمان اصلی تایید شده: دانشگاه شهید بهشتی (Shahid beheshti university)
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نشانی اینترنتی |
http://ijfs.usb.ac.ir/article_542_29a3205d0a54855da6b624d09f45be58.pdf |
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