|
|
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 |
| فایل مقاله |
فایلی برای مقاله ذخیره نشده است |
| کد مقاله (doi) |
|
| زبان مقاله منتشر شده |
fa |
| موضوعات مقاله منتشر شده |
|
| نوع مقاله منتشر شده |
|
|
|
|
برگشت به:
صفحه اول پایگاه |
نسخه مرتبط |
نشریه مرتبط |
فهرست نشریات
|