Fuzzy parametrized fuzzy soft topology

Abstract

Recently, researches have contributed a lot towards fuzzification of Soft Set Theory. In this paper, we introduce the topological structure of fuzzyfying soft sets called fuzzy parametrized fuzzy soft sets. We define the notion of quasi-coincidence for fuzzy parametrized fuzzy soft sets and investigated basic properties of it. We study the closure, interior, base, continuity and compactness in the content of fuzzy parametrized fuzzy soft topological spaces.

Certain Applications of Fuzzy Parameterized Fuzzy Soft Sets in Decision-Making Problems

“…Definition 2.2. [9,41] A fuzzy parameterized fuzzy soft set (FPFS-set) is a mapping γ : R → P(X) such that γ A (ζ) = φ if µ A (ζ) = 0, where X is the initial universe and A ⊆ R, R is the set of parameters or attributes. It is denoted by F A as given below Then FPFS-set is written by…”

“…Riaz et al [29][30][31] discussed various concepts including soft σ-algebra, measurable soft set, measurable soft mappings and soft metric spaces. Idris and Serkan [41] presented some interesting results on FPFS-topological space. Borah and Hazarika [7] discussed some properties of FS-topology and also established some applications in Chemistry.…”

A Data Classification Method in Machine Learning Based on Normalised Hamming Pseudo-Similarity of Fuzzy Parameterized Fuzzy Soft Matrices

“…Soft sets (Molodtsov, 1999), a standard and practical mathematical tool, are often used for modelling uncertainties, and a great variety of studies have been conducted on this concept (Çağman and Deli, 2012a, b;Deli and Çağman, 2015;Enginoğlu et al, 2015;Şenel, 2016;Zorlutuna and Atmaca, 2016;Atmaca, 2017;Çıtak and Çağman, 2017;Riaz and Hashmi, 2017;Atmaca, 2019;Çıtak, 2018;Şenel 2018a, b;Jana et al, 2019;Karaaslan, 2019a, b;Sezgin et al, 2019a, b). Fuzzy soft sets (Maji et al, 2001;Çağman et al, 2011b), fuzzy parameterized soft sets (Çağman et al, 2011a), and fuzzy parameterized fuzzy soft sets (fpfs-sets) (Çağman et al, 2010) are among known general forms of soft sets.…”

Fixed points of fuzzy neutrosophic soft mapping with decision-making

“…have various uncertainties. To deal with uncertainties there are different theories including the fuzzy set introduced by Zadeh [1], the soft set introduced by Molodtsov [2], the fuzzy soft set (fs-sets) [3] and the fuzzy parameterized fuzzy soft set (fpfs-sets) [4,5]. The intuitionistic fuzzy set (if-set) introduced by Atanassov [6], which is an abstraction of fuzzy set.…”

“…A soft set [2] is a mathematical tool to handle the uncertainties associated with real world data-based problems. Fuzzy parameterized fuzzy soft sets introduced in [4,5] provide a very interesting extension of fuzzy sets and soft sets. fpfs-sets provide a suitable degree of membership to both parameters and elements of the initial universe.…”