The concept of fuzzy idealistic soft Γ−rings is introduced, some properties of fuzzy idealistic soft Γ−rings are given. Then the definitions of (∈,∈ ∨q)−fuzzy idealistic soft Γ−rings and fuzzy prime idealistic soft Γ−rings are proposed, and some theory of them is considered.

The notion of soft BCI-implicative ideals and BCI-implicative idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft BCI-implicative ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and BCI-implicative idealistic soft BCI-algebras are being related. The intersection, union, “AND” operation and “OR” o...

The notion of soft BCI-commutative ideals and BCI-commutative idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft BCI-commutative ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and BCI-commutative idealistic soft BCI-algebras are being related. The intersection, union, “AND” operation and “OR” o...

The notions of (transitive) soft d-algebras, soft edge d-algebras, soft d-algebras, soft dideals, soft d-ideals, soft d-ideals, and d-idealistic (d-idealistic, or d-idealistic) soft dalgebras are introduced. Also, their related properties are surveyed. © 2008 Elsevier Ltd. All rights reserved.

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 BCKalgebras and implicative idealistic soft BCK-algebras is ...