On Topological Structures of Fuzzy Parametrized Soft Sets

Abstract

We introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated its basic properties. We study the closure, interior, base, continuity, and compactness and properties of these concepts in fuzzy parametrized soft topological spaces.

Bulanık Esnek Ditopolojiler Üzerine Bir Çalışma

“…Soft and fs-sets and the structures on these sets were observed by several researchers (Ahmad and Hussain, 2012, Atmaca and Zorlutuna, 2014, Aygunoglu and Aygun, 2011, Aygunoglu et. al., 2014, Bera et.al., 2017, Cagman and Aktas, 2011, Cagman et.…”

Notes on Fuzzy Parametrized Soft Sets

“…Definition 15 [23]The FP-soft set ̃∈ ( , ) is called FP-soft point if ̃ is fuzzy singleton and ( ) ∈ ( ) for ∈supp . If = { }, ( ) = ∈ (0,1], then we denote this FP-soft point by .…”

“…Definition 16 [23]Let ̃, ̃∈ ( , ). ̃ is said to be fp-quasi-coincident with ̃, denoted by ̃̃, if there exists ∈ such that ( ) + ( ) > 1 or ( ) is not subset of ( ).…”

“…Definition 18 [23]A FP-soft topological space is a pair ( , ) where is a nonempty set and is a family of FP-soft sets over satisfying the following properties:…”

“…Definition 19 [23]Let ( , 1 ) and ( , 2 ) be two FP-soft topological spaces. A FP-soft mapping : ( , 1 ) → ( , 2 ) is called FP-soft continuous if −1 (̃) ∈ 1 for all ̃∈ 2 .…”