On Soft Topology

Abstract

Soft set theory was introduced by Molodtsov in 1999. Until now many versions of it have been developed and applied to a lot of areas from algebra to decision making problems. One of these areas is Soft Topology [Çağman, N., Karataş, S., Enginoglu, S., Soft topology, Computers and Mathematics with Applications, 62, 351-358, 2011]. However, it has some difficulties and mistakes. In this paper, for further study on the soft topology, we have made fit this concept which is important for development of the concept of soft sets by decontaminating from its own inconsistencies. We finally discuss this concept later on works.

Configurations of Several Soft Decision-Making Methods to Operate in Fuzzy Parameterized Fuzzy Soft Matrices Space

“…The concept of soft sets proposed by Molodtsov [1] is among popular mathematical tools propounded to model problems involving uncertainties, and so far, many pure and applied studies have been conducted on this concept [2][3][4][5][6][7][8][9][10][11]. A soft set is the graphics of a function defined from a set of parameters to the universal set (the set of alternatives).…”

A Generalization of Fuzzy Soft Max-Min Decision-Making Method and Its Application to a Performance-Based Value Assignment in Image Denoising

“…propounded the concept of soft sets to deal with uncertainties and up to now many researchers have conducted various applied and theoretical studies thereon (Maji et al, 2001(Maji et al, , 2003Çağman and Enginoğlu, 2010a;Çağman et al, 2010;Çağman et al, 2011a,b;Deli and Çağman, 2015;Enginoğlu et al, 2015;Zorlutuna and Atmaca, 2016;Hashmi, 2017, 2018;Şenel, 2018;Ullah et al, 2018;Sezgin et al, 2019). To able to avail of the ability of this concept in computer mathematics (or sciences), Çağman and Enginoğlu presented the soft matrices (Çağman and Enginoğlu, 2010b) and fuzzy soft matrices (Çağman and Enginoğlu, 2012).…”

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.…”