Some soft topological properties and fixed soft element results in soft complex valued metric spaces

Demir, İzzettin

doi:10.3906/mat-2101-15

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…After Maji et al [10] and Ali et al [11] laid the foundations of the soft set operations, different interpretations have emerged about extending mathematical structures to the soft set theory (See [12][13][14][15][16][17][18], and others in them). The soft elements and elementary (ε-) soft set operations were brought forward by Das and Samanta [19], and some mathematical structures have been examined using these concepts by several authors [20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A Soft Set Approach to Relations and Its Application to Decision Making

Taşköprü

KARAKÖSE

2023

Mathematical Sciences and Applications E-Notes

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One of the most useful mathematical tools for examining the relationships among objects is the concept of relations. Besides, it can also be necessary to throw light on uncertainties in these relationships. Soft set theory, in which different approaches used in defining the notions bring about different applications in many areas, enables to overcome uncertainties. The purpose of this paper is to define soft relations in a different way and to give a decision making method using the concept of soft relations. For this purpose, firstly, the soft relations are defined on the collection of soft elements, unlike the previous ones. After their basic properties are provided, the correspondence between the soft relations and the classical relations is investigated and some examples are given. Finally, an algorithm is proposed using the soft relations for solving decision making problems, where the decision is related to other circumstances, and given an illustrative example.

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Section: Introductionmentioning

confidence: 99%

A Soft Set Approach to Relations and Its Application to Decision Making

Taşköprü

KARAKÖSE

2023

Mathematical Sciences and Applications E-Notes

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“…For a STS (U, τ, E), the members τ are called soft open sets. Soft topological concepts and their applications are still a hot area of research [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The concept of ω-open sets in TSs is defined in [23] as follows: let (U, ) be a TS and V ⊆ U, then V is ω-open set in (U, ) if for each x ∈ V, there is W ∈ such that x ∈ W and W − V is countable, or equivalently, V is ω-open set in (U, ) if and only if for each x ∈ V, there is W ∈ and a countable set C ⊆ U such that x ∈ W −C ⊆ V. Denote the family of all ω-open sets in the TS (U, ) by ω .…”

Section: Introductionmentioning

confidence: 99%

Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Ghour

2021

Mathematics

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In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

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Soft order topology and graph comparison based on soft order

Taşköprü

2023

MATH

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<abstract><p>Soft sets provide a suitable framework for representing and dealing with vagueness. A scenario for vagueness can be that alternatives are composed of specific factors and these factors have specific attributes. Towards this scenario, this paper introduces soft order and its associated order topology on the soft sets with a novel approach. We first present the definitions and properties of the soft order relations on the soft sets via soft elements. Next, we define soft order topology on any soft set and provide some properties of this topology. In order to implement what we introduced about the soft orders, we describe soft preference and soft utility mapping on the soft sets and we finally demonstrate a decision-making application over the soft orders intended for comparing graphs.</p></abstract>

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Some soft topological properties and fixed soft element results in soft complex valued metric spaces

Cited by 3 publications

References 15 publications

A Soft Set Approach to Relations and Its Application to Decision Making

A Soft Set Approach to Relations and Its Application to Decision Making

Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Soft order topology and graph comparison based on soft order

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