On Fuzzy Ordered Abel-Grassmann's Groupoids

Madad Khan, Faisal Faisal


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 in
terms 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 a
semilattice 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.

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DOI: http://dx.doi.org/10.5539/jmr.v3n2p27

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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