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Iranian Journal of Fuzzy Systems، جلد ۶، شماره ۴، صفحات ۷۳-۸۷
عنوان فارسی SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS
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.
کلیدواژه‌های فارسی مقاله Generalized groups، Fuzzy generalized subgroups، t-norm، Heyting algebra،
عنوان انگلیسی SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS
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.
کلیدواژه‌های انگلیسی مقاله Generalized groups, Fuzzy generalized subgroups, t-norm, Heyting algebra
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)

نشانی اینترنتی http://ijfs.usb.ac.ir/article_542_29a3205d0a54855da6b624d09f45be58.pdf
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