Naveed Yaqoob, Muhammad Aslam, Inayatur Rehman, and Mohammed M. Khalaf

DOI: 10.14456/sjst-psu.2016.16

pp. 119 - 127

Abstract

The notion of bipolar fuzzy set was initiated by Lee (2000) as a generalization of the notion fuzzy sets and intuitionistic fuzzy sets, which have drawn attention of many mathematicians and computer scientists. In this paper, we initiate a study
on bipolar ( λ,δ )-fuzzy sets in Γ-semihypergroups. By using the concept of bipolar ( λ,δ )-fuzzy sets (Yaqoob and Ansari,
2013), we introduce the notion of bipolar ( λ,δ )-fuzzy sub Γ-semihypergroups (Γ-hyperideals and bi-Γ-hyperideals) and
discuss some basic results on bipolar ( λ,δ )-fuzzy sets in Γ-semihypergroups. Furthermore, we define the bipolar fuzzy
subset ß_λ^δ = ⟨µ⁺ ß_λ^δ , µ^- ß_λ^δ⟩
and prove that if ß = ⟨µ⁺_ß ,µ^- _ß⟩
is a bipolar ( λ,δ )-fuzzy sub  Γ-semihypergroup (resp.,  Γ-hyperideal
and bi- Γ-hyperideal) of H; then ß_λ^δ = ⟨µ⁺ ß_λ^δ , µ^- ß_λ^δ⟩
is also a bipolar (λ,δ )-fuzzy sub Γ-semihypergroup (resp., Γ-hyperideal
and bi-Γ-hyperideal) of H.