(na, nb) bipolar valued intuitionistic fuzzy ideals of an ordered Γ-semigroups

Abstract

The concept of (na, nb) bipolar valued intuitionistic fuzzy subsemigroup (BVIntSS), left ideal (BVIntLI), right ideal (BVIntRI), ideal (BVIntI) and bi-ideal (BVIntBI) of an ordered Γ-semigroups are introduced in this paper, along with some of their characteristics. A novel extension of the BVIntI over ordered Γsemigroups O is the notion of (na, nb) BVIntI. A (na, nb)-BVIntSS (BVIntLI, BVIntRI, BVIntBI) of O is a non-empty subset ζna n . Consequently, O’s lower level set Λ n nn is an SS(BVLI, BVRI, BVBI). A subset ζ = [(Λn,Λ p ),(Σn, Σ p )] is a (na, nb) BVIntSS[BVIntLI,BVIntRI,BVIntBI] of O if and only if each nonempty level subset ζ(t,s) is a BVSS [BVLI,BVRI,BVBI] of O for every t ∈ (nn a , nn b ] and s ∈ [np a , n p b ]. Every (na, nb)BVIntSS is a BVIntSS of O, but the opposite is not true. Examples are included to demonstrate our findings.