some properties of t-fuzzy generalized subgroups

in this paper, we deal with molaei’s 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.