A New Type of Interval Valued Fuzzy Normal Subgroups of Groups
Journal: NEW TRENDS IN MATHEMATICAL SCIENCES (Vol.3, No. 1)Publication Date: 2015-03-01
Authors : Saleem Abdullah; Muhammad Naeem;
Page : 62-77
Keywords : Group normal subgroup coset interval valued -fuzzy normal subgroup interval valued -fuzzy coset.;
Abstract
In this paper we are using the notions of not belonging and non quasi- -coincidence of an interval valued fuzzy point with an interval valued fuzzy set, we define the concepts of interval valued -fuzzy normal subgroups and interval valued -fuzzy cosets which is a generalizati on of fuzzy normal subgroups, fuzzy coset, interval valued fuzzy normal subgroups, interval valued fuzzy coset, interval valued -fuzzy normal subgroups and interval valued -fuzzy cosets. We give some characterizations of an interval valued -fuzzy normal subgroup and interval valued -fuzzy coset, and deal with several related properties. The important achievement of the study with an interval valued -fuzzy normal subgroup and interval valued -fuzzy cosets is the generalization of that the notions of fuzzy normal subgroups, fuzzy coset, interval valued fuzzy normal subgroups, interval valued fuzzy coset, interval valued -fuzzy normal subgroups and interval valued -fuzzy cosets. We prove that the set of all interval valued -fuzzy cosets of is a group, where the multiplication is defined by for all If is defined by for all Then is an interval valued -fuzzy normal subgroup of
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