Fuzzy Abel Grassmann's Groupoids
Abstract
In the present paper we have studied the concept of fuzzification in AG-groupoids. The equivalent statement for an AG-groupoid to be a commutative semigroup is proved. Fuzzy points have been defined in an AG-groupoid and has been shown the representation of smallest fuzzy left ideal generated by a fuzzy point. The set of all fuzzy left ideals, which are idempotents, forms a commutative monoid. The relation of fuzzy left(right) ideals, fuzzy interior ideals and fuzzy bi-ideals in AG-groupoid has been studied. Necessary and sufficient condition of fully fuzzy prime AG-groupoid has been shown. Further, It has been shown that the set of fuzzy quasi-prime ideals of AG-groupoid with left identity forms a semillattice structure. Moreover, equivalent statements for fuzzy semiprime left ideal in an AG-groupoid have been proved.
Cite
@article{arxiv.0904.0077,
title = {Fuzzy Abel Grassmann's Groupoids},
author = {Madad Khan and Muhammad Nouman Aslam Khan},
journal= {arXiv preprint arXiv:0904.0077},
year = {2009}
}
Comments
9 pages