We have defined fuzzy bipolar soft sets and basic operations of union, intersection and complementation for fuzzy bipolar soft sets. The algebraic properties of fuzzy bipolar soft sets are discussed. The concept of bipolar fuzzy soft set is also given and the equivalence of both structures is established. An application of fuzzy bipolar soft sets in decision making problems is presented with th...

Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension to the soft set and intuitionistic fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy soft sets to semigroup theory. The notion of intuitionistic fuzzy soft ideals over a semigroup is introduced and their basic properties are investigated. Some lattice structures of the set of all int...

Firstly, soft hyperideals of hyperlattices are introduced and several interesting examples of them are given. Secondly, fuzzy soft hyperideals are proposed, which are generalizations of hyperideals and soft hyperideals in hyperlattices. After that, equivalent conditions of fuzzy soft hyperideals are given by using level soft sets. Finally, under the fuzzy soft homomorphism of hyperlattices, the...

Molodtsov first proposed the soft set theory, which can be used as a general mathematical tool for dealing with fuzzy and uncertain information. As a generalization of soft set, interval-valued intuitionistic fuzzy soft set is another soft set structure,it is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The objective of this paper is to study the decision making ...

Research on soft set based decision making has received much attention in recent years. Feng et al. presented an adjustable approach to fuzzy soft sets based decision making by using level soft set, and subsequently extended the approach to interval-valued fuzzy soft set based decision making. Jiang et al. generalize the approach to solve intuitionistic fuzzy soft sets based decision making. In...

In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈∨q)fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established.

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 aim of this paper is to apply the concept of fuzzy soft sets over a Γ -semigroup. Here the notion of fuzzy soft ideals over a Γ -semigroup has been introduced. The special union, intersection and product of fuzzy soft ideals over a Γ -semigroup have been defined and proved that these are also fuzzy soft Γ -ideals over the Γ -semigroup.