Characterization of Bipolar Fuzzy Soft Γ-Semigroups

Muhammad Akram; Jacob Kavikumar and Azme Bin Khamis

doi:10.17485/ijst/2014/v7i8.18

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Characterization of Bipolar Fuzzy Soft Γ-Semigroups

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2014/v7i8.18

Year: 2014, Volume: 7, Issue: 8, Pages: 1211–1221

Original Article

Characterization of Bipolar Fuzzy Soft Γ-Semigroups

Muhammad Akram^* , Jacob Kavikumar and Azme Bin Khamis

Department of Mathematics and Statistic, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Johor, Malaysia; makram_69@yahoo.com, kaviphd@gmail.com, azme@uthm.edu.my

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

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.

Keywords: Bipolar Fuzzy Soft Set, Bipolar Fuzzy Soft Γ-subsemigroup, Bipolar Fuzzy Soft Γ-ideals.