Ordered semigroups characterized by interval valued ε, ε $\vee$ q-fuzzy bi-ideals

Authors:
Asghar Khan;Young Bae Jun;Muhammad Shabir
Affiliations:
Department of Mathematics, COMSATS Institute of Information Technology, KPK, Abbottabad, Pakistan;Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, Korea;Department of Mathematics, Quaid-i-Azam University, Islambad, Pakistan
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2013

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Abstract

In this article, we first introduce the concept of quasi-coincidence of an interval valued fuzzy point with an interval valued fuzzy subset. This concept is a generalization of the concept of quasi-coincidence of a fuzzy point within a fuzzy subset. By using this new idea, we introduce the concept of an interval valued α, β-fuzzy bi-ideals in ordered semigroups. Which is a generalization of the idea of an α, β-fuzzy bi-ideals in ordered semigroups. Some interesting results of the algebraic ordered semigroups in terms of interval valued α, β-fuzzy bi-ideals are given. By using interval valued $ε, ε $\vee$ q-fuzzy bi-ideals some interesting results are obtained.