Affiliations: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan | Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia | Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia | Department of Mathematics, Yazd University, Yazd, Iran | Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt
Note: [] Corresponding author. N. Yaqoob, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan. E-mail: [email protected]
Abstract: The theory of bipolar fuzzy sets introduced by Lee [9] has been applied to many branches of mathematics. In this paper, we initiate a study on bipolar fuzzy sets in Γ-semihypergroups. We define bipolar fuzzy left (right, bi-, interior, (1,2)-) Γ-hyperideals and explore some related properties. We use these bipolar fuzzy Γ-hyperideals to characterize some classes of Γ-semihypergroups. We consider the Γ-semihypergroup $\underline{\mathcal{H}}$ of the bipolar fuzzy points of a Γ-semihypergroup H to discuss the relation between the bipolar fuzzy sub Γ-semihypergroup (left, right, bi-, interior, (1,2)-) Γ-hyperideal and the subsets of $\underline{\mathcal{H}}$ in a (regular) Γ-semihypergroup. In the end, we discuss in detail a number of results on homomorphic images and preimages of bipolar fuzzy Γ-hyperideals.
