Abstract
In this paper, we introduce the concept of bipolar fuzzy soft gamma hyperideals in gamma hyper semigroups. We define bipolar fuzzy soft hyper ideals, bi-ideals and interior ideals of gamma hyper semigroups and discuss some properties.
Highlights
Zadeh [18] introduced the concept of fuzzy sets in 1965
Algebraic hyper structures represent a natural extension of classical algebraic structures, and they were originally proposed in 1934 by Marty [7]
The concept of bipolar fuzzy soft sets has been introduced by Naz et al [12]
Summary
Zadeh [18] introduced the concept of fuzzy sets in 1965. Algebraic hyper structures represent a natural extension of classical algebraic structures, and they were originally proposed in 1934 by Marty [7]. Zhang [19] introduced the notion of bipolar fuzzy sets. The concept of bipolar fuzzy soft sets has been introduced by Naz et al [12]. Bipolar fuzzy soft Γ-semigroups was introduced by Muhammad Akram et al [10]. We define a new notion of bipolar fuzzy soft Γ- hyper semigroups and investigate some of its properties with examples. Let be a non empty subset of the pair is called a soft set over , where is a mapping given by Definition 2.6. The set of all fuzzy subset of is called the fuzzy power set of and is denoted by Definition 2.7[4]. Let and denotes the set of all bipolar fuzzy subsets of. A pair is called a bipolar fuzzy soft sets over , where is a mapping given by
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