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On Fuzzy Subgroups On Fuzzy Spaces



Using the concept of fuzzy space introduced by Dib in [2], we defined two new fuzzy subspaces, standard fuzzy subspace, denoted by S, and adjoint fuzzy subspace, denoted by and hence some new algebraic structures are studied. Necessary and sufficient conditions are given so that both fuzzy subspaces to be fuzzy subgroups. The relation between the fuzzy cosets of a fuzzy subgroup and the cosets of the adjoint fuzzy subgroup is given. The normality of both fuzzy subgroups S and is studied. Many isomorphism theorems for a fuzzy subgroup and the corresponding adjoint fuzzy subgroup are studied. Also, the notion of solvability of a fuzzy group is given via the definition of the commutator fuzzy subgroup. Many algebraic properties for S and are studies too.


Fuzzy space, Fuzzy groups, Fuzzy adjoint subspace, Fuzzy commutator

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