In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy ...

This paper investigates roughness of fuzzy soft sets. A pair of fuzzy soft rough approximations is proposed and their properties are given. Based on fuzzy soft rough approximations, the concept of fuzzy soft rough sets is introduced. New types of fuzzy soft sets such as full, intersection complete and union complete fuzzy soft sets are defined and supported by some illustrative examples. We obt...

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...

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in amedical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised...

Soft set theory was introduced by Molodtsov in 1999 as a general mathematical tool for dealing with problems that contain uncertainty. In this paper, we define concept of fuzzy soft lattice, fuzzy soft sublattice, complete fuzzy soft lattice, modular fuzzy soft lattice, distributive fuzzy soft lattice, fuzzy soft chain and study their basic properties.

In the present paper, we study and investigate the properties of fuzzy soft α-connected sets, fuzzy soft α-separated sets and fuzzy soft α-s-connected sets and establish several interesting properties supported by examples. Moreover, we show that, a fuzzy soft α-disconnectedness is not an hereditary property in general. Finally, we show that the fuzzy α-irresolute surjective soft image of fuzzy...

In this paper, we present the concepts of a fuzzy soft left (right) ideal and fuzzy soft interior ideal over an ordered semigroup S . Some basic results of fuzzy soft left (right) ideals and fuzzy soft interior ideals are investigated and the supported examples are provided. Different classes, regular, intra-regular, and simple ordered semigroups are characterized by means of fuzzy soft left (r...