On Fuzzy Ordered Abel-Grassmann's Groupoids

In this paper, we have introduced the concept of fuzzy ordered AG-groupoids which is the generalization of fuzzy ordered semigroups first considered by Kehayopulu and Tsingelis (2002). We have studied some important features of a left regular ordered AG-groupoid interms of fuzzy left ideals, fuzzy right ideals, fuzzy two-sided ideals, fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy (1,2)-ideals. We have shown that the set of all fuzzy two-sided ideals of a left regular ordered AG-groupoid forms asemilattice structure. We have characterized all the fuzzy ideals of a left regular ordered AG-groupoid. Finally we have characterized a left regular ordered AG-groupoid by their fuzzy left and fuzzy right ideals.