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 Union-soft sets with applications in $BCK/BCI$-algebras Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 1937-1956 https://doi.org/10.4134/BKMS.2013.50.6.1937Published online November 1, 2013 Young Bae Jun Gyeongsang National University Abstract : The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. 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. Keywords : exclusive set, union-soft algebra, (closed) union-soft ideal, union-soft commutative ideal MSC numbers : 06F35, 03G25, 06D72 Downloads: Full-text PDF