The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real an...

In recent years, soft sets have become popular in various fields. For this reason, many studies been carried out the field of algebra. study, intersection k-ideals are defined with help a semiring, and some algebraic structures examined. Moreover, quotient rings by k-semiring. Isomorphism theorems examined rings. Finally, properties investigated defining maximal k-ideals.

We introduce the concepts soft β-interior and soft β-closure of a soft set in soft topological spaces. We also study soft β-continuous functions and discuss their relations with soft continuous and other weaker forms of soft continuous functions.

The central objective of the proposed work in this research is to introduce innovative concept an m-polar fuzzy set (m-PFS) semigroups, that is, expansion bipolar (BFS). Our main focus study generalization some important results BFSs m-PFSs. This paper provides related subsemigroups (m-PFSSs), ideals (m-PFIs), generalized bi-ideals (m-PFGBIs), (m-PFBIs), quasi-ideals (m-PFQIs) and interior (m-P...

In this paper the concept of interval valued intuitionistic fuzzy soft topological space(IVIFS topological space) together with interval valued intuitionistic fuzzy soft open sets(IVIFS open sets) and interval valued intuitionistic fuzzy soft closed sets(IVIFS closed sets) are introduced. We define neighbourhood of an IVIFS set, interior IVIFS set, interior of an IVIFS set, exterior IVIFS set, ...

As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (c...