New types of bipolar fuzzy sets in -semihypergroups

• Main Authors: Naveed Yaqoob, Muhammad Aslam, Inayatur Rehman, Mohammed M. Khalaf
• Format: Article
• Language: English
• Published: Prince of Songkla University 2016-04-01
• Series: Songklanakarin Journal of Science and Technology (SJST)
• Subjects: -semihypergroups; bipolar fuzzy sets; )-fuzzy -hyperideals; bipolar ( 
• Online Access: http://rdo.psu.ac.th/sjstweb/journal/38-2/38-2-1.pdf

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 ( , )-fuzzy sets in -semihypergroups. By using the concept of bipolar ( , )-fuzzy sets (Yaqoob and Ansari, 2013), we introduce the notion of bipolar ( , )-fuzzy sub -semihypergroups (-hyperideals and bi--hyperideals) and discuss some basic results on bipolar ( , )-fuzzy sets in -semihypergroups. Furthermore, we define the bipolar fuzzy subset ,               and prove that if  ,       is a bipolar ( , )-fuzzy sub -semihypergroup (resp., -hyperideal and bi--hyperideal) of H; then ,               is also a bipolar ( , )-fuzzy sub -semihypergroup (resp., -hyperideal and bi--hyperideal) of H.