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The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncer- tainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are introduced, and related properties and relations are investigated. Conditions for a union-soft ideal to be closed are provided. Conditions for a union-soft ideal to be a union-soft commutative ideal are also provided. Characterizations of (closed) union- soft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.

UNION-SOFT SETS WITH APPLICATIONS IN BCK/BCI-ALGEBRAS