A new kind of soft algebraic structures: bipolar soft Lie algebras

Abstract

In this paper, basic concepts of soft set theory was mentioned. Then, bipolar soft Lie algebras and bipolar soft Lie ideals were defined with the help of soft sets. Some algebraic properties of the new concepts were investigated. The relationship between the two structures were analyzed. Also, it was proved that the level cuts of a bipolar soft Lie algebra were Lie subalgebras of a Lie algebra by the new definitions. After then, soft image and soft preimage of a bipolar soft Lie algebra/ideal were proved to be a bipolar soft Lie algebra/ideal.