Characterization of Bipolar Fuzzy Soft Ã-semigroups

This paper deals with the idea of bipolar fuzzy soft sets applied to the ideal theory of τ-semigroups. We have introduced the concept of bipolar fuzzy soft τ-subsemigroup and bipolar fuzzy soft τ-ideals in a τ-semigroup. It is proved that the extended union, extended intersection, restricted union and restricted intersection of two same kind bipolar fuzzy soft τ-ideals over a τ-semigroup produced a same kind's bipolar fuzzy soft τ-ideal. Also the "AND" and "OR" operations of two bipolar fuzzy soft Ã-ideals produced a same type's bipolar fuzzy soft τ-ideal. It is also proved that the collection of all bipolar fuzzy soft τ-ideals over a τ-semigroup forms a complete distributive lattice with these special unions and intersections.