Γ-Abel-Grassmann's groupoids characterized by their intuitionistic Γ-ideals

Details Γ-Abel-Grassmann's groupoids characterized by their intuitionistic Γ-ideals Γ-Abel-Grassmann's groupoids characterized by their intuitionistic Γ-ideals

2010-11-12

arxiv.org/abs/1011.2845v1

Mathematics

Group Theory

Scientific paper

In this paper, we have discussed several properties of intuitionistic fuzzy {\Gamma}-ideals of a {\Gamma}-AG-groupoid which is the generalization of ideals in AG-groupoid We have characterized an intra-regular {\Gamma}-AG^{**}-groupoid in terms of intuitionistic fuzzy {\Gamma}-left (right, two-sided) ideals, intuitionistic fuzzy ({\Gamma}-generalized bi) {\Gamma}-bi-ideals, intuitionistic fuzzy {\Gamma}-interior ideals and intuitionistic fuzzy {\Gamma}-quasi ideals. We have proved that the intuitionistic fuzzy {\Gamma}-left (right, interior, quasi) ideals coincide in an intra-regular {\Gamma}-AG^{**}-groupoid. We have also shown that the set of intuitionistic fuzzy {\Gamma}-two-sided ideals of an intra-regular {\Gamma}-AG^{**}-groupoid forms a semilattice structure.

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