Document Type: Research Paper


1 Department of Mathematics, University of Bojnord, Bojnord, Iran

2 Department of Mathematics, Shahid Beheshti University, Tehran, Iran


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.


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