This paper deals with the idea of bipolar fuzzy soft sets applied to the ideal theory of Γ-semigroups. We have introduced the concept of bipolar fuzzy soft Γ-subsemigroup and bipolar fuzzy soft Γ-ideals in a Γ-semigroup. It is proved that the extended union, extended intersection, restricted union and restricted intersection of two same kind bipolar fuzzy soft Γ-ideals over a Γ-semigroup produced a same kind’s bipolar fuzzy soft Γ-ideal. Also the “AND” and “OR” operations of two bipolar fuzzy soft Γ-ideals produced a same type’s bipolar fuzzy soft Γ-ideal. It is also proved that the collection of all bipolar fuzzy soft Γ-ideals over a Γ-semigroup forms a complete distributive lattice with these special unions and intersections.
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Muhammad Akram (2014) studied this question.
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