On Anti Fuzzy Ideals in Left Almost Semigroups

Madad Khan, M. Faisal Iqbal, M. Nouman A. Khan

Abstract


In this paper we have studied the concept of Anti fuzzy ideals in Left Almost Semigroups (LA-semigroup in short). The equivalent statement for an LA-semigroup to be a commutative semigroup is proved. The set of all anti fuzzy left ideals, which are idempotents, forms a commutative monoid. Moreover it has been shown that the union of any family of Anti fuzzy left ideals of an LA-semigroup is an anti fuzzy left ideal of F(S). The relation of anti fuzzy left(right) ideals, anti fuzzy interior ideals and anti fuzzy bi-ideals in LA-semigroups has been studied. Anti fuzzy points have been defined in an LA-semigroup and has been shown the representation of largest fuzzy left ideal generated by a fuzzy point.

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

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