Communications of the
Korean Mathematical Society CKMS

Molodtsov [5] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to an implicative ideal of BCK-algebras. The notion of implicative soft ideals in BCK-algebras and implicative idealistic soft BCK-algebras is introduced, and related properties are investigated. Relations between implicative soft ideals and commutative (resp. positive implicative) soft ideals are discussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

Keywords: soft BCK-algebra, (implicative, commutative, positive implicative) soft ideal, (implicative, commutative, positive implicative) idealistic soft BCK-algebra

MSC numbers: 06D72, 06F35, 03G25