New types of bipolar fuzzy sets in -semihypergroups

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 ( , )-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.

Keywords

• -semihypergroups
• bipolar fuzzy sets
• )-fuzzy -hyperideals
• bipolar ( 
• )-fuzzy -hyperideals