Categories Related to Topology Viewed as Soft Sets

Abstract

D. Molodtsov (1999) introduced the concept of a soft set as a new approach for modeling uncertainties. The aim of this work is to define special kinds of soft sets, namely soft, L-fuzzifying soft, L-soft, and L-fuzzy soft neighborhood sets and to use them in order to give an alternative characterization of categories related to topology: crisp topological, L-topological, L-fuzzifying topological and L-fuzzy topological spaces.

A categorical approach to soft S-acts

“…Clearly, every soft homomorphism is a weak soft homomorphism. Note that in some papers the weak condition "G( (a)) ⊆ f (F(a)) for all a ∈ A" has been considered as the definition of soft mapping (see, for example, [18]). If ( f, ) : (F, A) A → (G, B) B and (h, k) : (G, B) B → (H, C) C are soft homomorphisms, then the soft composition of ( f, ) and (h, k) is defined as (h, k)( f, ) = (p, q) : (F, A) A → (H, C) C where p = h f and q = k .…”

A Soft Approach to Ring-Groupoids

“…It, which was initiated by Molodtsov in 1999, has been worked on many areas including mathematics. The boundaries of this theory, which attracted a great interest of mathematicians, have been expanded in algebraic, topological and categorical sense [2][3][4][5][6][7][8][9][12][13][14].…”

“…Recently, categorical studies on soft theory have been carried out. We refer to [12][13][14] for these studies. The definition of soft category was first proposed by Sardar and Gupta [12].…”

Categorical Properties of Soft Sets

“…Sardar and Gupta [ 35 ] defined another soft category which is a parameterized family of subcategories of a category. Varol et al [ 36 ] defined a new category of soft sets and soft mapping. These studies have presented a preliminary, but potentially interesting, research direction.…”