Bakhshi, M., Borzooei, R. (2009). SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS. Iranian Journal of Fuzzy Systems, 6(4), 73-87. doi: 10.22111/ijfs.2009.542

Mahmood Bakhshi; Rajab Ali Borzooei. "SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS". Iranian Journal of Fuzzy Systems, 6, 4, 2009, 73-87. doi: 10.22111/ijfs.2009.542

Bakhshi, M., Borzooei, R. (2009). 'SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS', Iranian Journal of Fuzzy Systems, 6(4), pp. 73-87. doi: 10.22111/ijfs.2009.542

Bakhshi, M., Borzooei, R. SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS. Iranian Journal of Fuzzy Systems, 2009; 6(4): 73-87. doi: 10.22111/ijfs.2009.542

^{1}Department of Mathematics, University of Bojnord, Bojnord, Iran

^{2}Department of Mathematics, Shahid Beheshti University, Tehran, Iran

Abstract

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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