University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06546420091222SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPSSOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS738754210.22111/ijfs.2009.542ENMahmoodBakhshiDepartment of Mathematics, University of Bojnord, Bojnord,
IranRajab AliBorzooeiDepartment of Mathematics, Shahid Beheshti University, Tehran,
IranJournal Article20091222In this paper, we deal with Molaeiās generalized groups. We define<br />the notion of a fuzzy generalized subgroup with respect to a t-norm (or<br />T-fuzzy generalized subgroup) and give some related properties. Especially,<br />we state and prove the Representation Theorem for these fuzzy generalized<br />subgroups. Next, using the concept of continuity of t-norms we obtain a correspondence<br />between TF(G), the set of all T-fuzzy generalized subgroups of a<br />generalized group G, and the set of all T-fuzzy generalized subgroups of the<br />corresponding quotient generalized group. Subsequently, we study the quotient<br />structure of T-fuzzy generalized subgroups: we define the notion of a<br />T-fuzzy normal generalized subgroup, give some related properties, construct<br />the quotient generalized group, state and prove the homomorphism theorem.<br />Finally, we study the lattice of T-fuzzy generalized subgroups and prove that<br />TF(G) is a Heyting algebra.https://ijfs.usb.ac.ir/article_542_29a3205d0a54855da6b624d09f45be58.pdf