(α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets

Abstract

Bipolar fuzzy soft set theory, which is a very useful hybrid set in decision making problems, is a mathematical model that has been emphasized especially recently. In this paper, the concepts of (α,β)-cuts, first type semi-strong (α,β)-cuts, second type semi-strong (α,β)-cuts, strong (α,β)-cuts, inverse (α,β)-cuts, first type semi-weak inverse (α,β)-cuts, second type semi-weak inverse (α,β)-cuts and weak inverse (α,β)-cuts of bipolar fuzzy soft sets were introduced together with some of their properties. In addition, some distinctive properties between (α,β)-cuts and inverse (α,β)-cuts were established. Moreover, some related theorems were formulated and proved. It is further demonstrated that both (α,β)-cuts and inverse (α,β)-cuts of bipolar fuzzy soft sets were useful tools in decision making.

Keywords

• Bipolar soft set
• bipolar fuzzy soft set
• (α,β)-cut
• inverse(α,β)-cut

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