An Introduction to Fuzzy Soft Topological Spaces

Abstract

The aim of this study is to define fuzzy soft topology which will be compatible to the fuzzy soft theory and investigate some of its fundamental properties. Firstly, we recall some basic properties of fuzzy soft sets and then we give the definitions of cartesian product of two fuzzy soft sets and projection mappings. Secondly, we introduce fuzzy soft topology and fuzzy soft continuous mapping. Moreover, we induce a fuzzy soft topology after given the definition of a fuzzy soft base. Also, we obtain an initial fuzzy soft topology and give the definition of product fuzzy soft topology. Finally, we prove that the category of fuzzy soft topological spaces FSTOP is a topological category over SET.

L- Fuzzy (K,e)-Soft Quasi Uniform Spaces and L-Fuzzy (K,e)-Soft Topogenous Spaces

“…[3,5,23] A map f is called an L-fuzzy soft set on X, where f is a mapping from E into L X , i.e., f e := f (e) is an L-fuzzy set on X, for each e ∈ E. The family of all L-fuzzy soft sets on X is denoted by (L X ) E . Let f and g be two L-fuzzy soft sets on X.…”

“…Later, Maji et al [15] introduced the concept of a fuzzy soft set which combines a fuzzy set and a soft set. Presently, the soft set theory is making progress rapidly [1,2,6,[15][16][17][18][19]26,28,31,32]. The topological structures of soft sets have been developed by many researchers [3,5,8,23,27,29,30,33].…”

Soft structures of groups and rings

“…In 2007, Aktas and Cagman [2] initiated an algebraic structure in a soft set, known as soft group. Extending this notion of soft group, many authors defined other algebraic structures like soft (ring, field, ideal) and hybrid structures like fuzzy soft (ring, field, ideal), intuitionistic fuzzy soft structures, rough soft structures (see [1], [4], [6]- [9]) etc. In 2013, Wardowski [14] introduced the notion of soft elements of a soft set.…”

$L$-Fuzzy $(K,e)$-Soft Topologies and $L$-Fuzzy $(K,e)$-Soft Closure Operators Induced by Fuzzy Soft Maps

“…In 2003, Maji et al [11] defined and studied several basic notions of soft set theory. Many researchers have contributed towards the algebraic structure of soft set theory [1][2][3][4][5]7]. In 2011, Shabir and Naz [19] initiated the study of soft topological spaces.…”