Characterizations of Abel-Grassmann's groupoids by their intuitionistic fuzzy ideals

Details Characterizations of Abel-Grassmann's groupoids by their intuitionistic fuzzy ideals Characterizations of Abel-Grassmann's groupoids by their intuitionistic fuzzy ideals

2010-10-14

arxiv.org/abs/1010.2910v1

Mathematics

Group Theory

Scientific paper

In this paper, we have introduced the concept of intuitionistic fuzzy ideals in an AG-groupoids. We have characterized regular and intra-regular AG-groupoids in terms of intuitionistic fuzzy left (right, two-sided) ideals, fuzzy (generalized) bi-ideals and intuitionistic fuzzy (1,2)-ideals. We have proved that all the intuitionistic fuzzy ideals coincides in regular and intra-regular AG-groupoids. It has been shown that the set of intuitionistic fuzzy two sided ideals of a regular AG-groupoid forms a semilattice structure. We have also given some useful conditions for an AG-groupoid to become an intra-regular AG-groupoid in terms their intuitionistic fuzzy ideals.

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