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
Note: [] Corresponding author. Asghar Khan, Department of Mathematics, COMSATS Institute of Information Technology, KPK, Abbottabad, Pakistan. E-mails: azhar4set@yahoo.com (Asghar Khan); skywine@gmail.com (Young Bae Jun); mshabirbhatti@yahoo.co.uk (Muhammad Shabir).
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.
