%0 Journal Article
%T SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Bakhshi, Mahmood
%A Borzooei, Rajab Ali
%D 2009
%\ 12/22/2009
%V 6
%N 4
%P 73-87
%! SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS
%K Generalized groups
%K Fuzzy generalized subgroups
%K t-norm
%K Heyting
algebra
%R 10.22111/ijfs.2009.542
%X In this paper, we deal with Molaeiās generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of all T-fuzzy generalized subgroups of ageneralized group G, and the set of all T-fuzzy generalized subgroups of thecorresponding quotient generalized group. Subsequently, we study the quotientstructure of T-fuzzy generalized subgroups: we define the notion of aT-fuzzy normal generalized subgroup, give some related properties, constructthe quotient generalized group, state and prove the homomorphism theorem.Finally, we study the lattice of T-fuzzy generalized subgroups and prove thatTF(G) is a Heyting algebra.
%U https://ijfs.usb.ac.ir/article_542_29a3205d0a54855da6b624d09f45be58.pdf