Bipolar Soft Generalized Topological Structures and  Their Application in Decision Making

Saleh, Hind; Asaad, Baravan A.; Mohammed, Ramadhan A.

doi:10.29020/nybg.ejpam.v15i2.4353

Cited by 5 publications

(9 citation statements)

References 19 publications

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“…Definition 2.14 [43] Let g be the class of BSSs, then g is called a bipolar soft generalized topology (BSGT ) on Ω if the following conditions are satisfying:…”

Section: It Is Denoted Bymentioning

confidence: 99%

“…Proposition 2.2 [43] Let (Ω, g, ϱ, ¬ϱ) be a BSGT S. Then the class g ς = {Λ(ς) : (Λ, Θ, ϱ) ∈ g} for each ς ∈ ϱ, defines a soft generalized topology on Ω.…”

Section: It Is Denoted Bymentioning

confidence: 99%

“…In [43], the concepts of BS g-interior set, BS g-closure set, BS g-exterior set and BS g-boundary set are defined and some of their results are investigated. In this section, we will give more results among these concepts via BSPs on the BSGT Ss.…”

Section: Bs G-limit Points In Bsgt Smentioning

confidence: 99%

“…Öztürk [42] introduced the point concept on bipolar soft set structure, fundamental properties for this point concept are presented. In 2022, Saleh, Asaad and Mohammed [43] defined a bipolar soft generalized topological space (BSGT S) and they introduced some topological structures such as BS g-interior, BS g-closure, BS g-exterior and BS g-boundary sets.…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 2.1 [43] Let (Ω, g, ϱ) be a SGT . Then g is the class including BSSs (Λ, Θ, ϱ) in which (Λ, ϱ) ∈ g and Θ(¬ϱ) = Ω \ Λ(ς) for all ς ∈ ϱ and ¬ς ∈ ¬ϱ defines a BSGT on Ω.…”

mentioning

confidence: 99%

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Bipolar Soft Limit Points in Bipolar Soft Generalized Topological Spaces

Saleh¹,

Asaad²,

Mohammed³

2022

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The concept of soft set theory can be used as a mathematical tool for dealing with problems that contain uncertainty. Then, a new mixed mathematical model called the bipolar soft set is created by merging soft sets and bipolarity, which gave the concept of a binary model of grading. Bipolar soft set is characterized by two soft sets, one of which provides positive information and the other negative. Bipolar soft generalized topology is a generalization of bipolar soft topology. The importance of limit points in all branches of mathematics cannot be ignored. It forms one of the most significant and fundamental concepts in topology. On this basis, the derived set concept is required in the establishment and continuation of some properties. Accordingly, the limit point in bipolar soft generalized theory is defined. In this paper, we present the notion of bipolar soft generalized limit points. We explained the relation between the bipolar soft generalized derived and the bipolar soft generalized closure set. Added to that, we discussed some structures of a bipolar soft generalized topological space such as: BS g-interior point, BS g-exterior point, BS g-boundary point, BS g-neighborhood point and basis on BSGT S. Finally, we give comparisons among these concepts of bipolar soft generalized topological spaces (BSGT S) by using bipolar soft point (BSP). Each concept introduced in this paper is explained with clear examples.

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“…Definition 2.14 [43] Let g be the class of BSSs, then g is called a bipolar soft generalized topology (BSGT ) on Ω if the following conditions are satisfying:…”

Section: It Is Denoted Bymentioning

confidence: 99%

“…Proposition 2.2 [43] Let (Ω, g, ϱ, ¬ϱ) be a BSGT S. Then the class g ς = {Λ(ς) : (Λ, Θ, ϱ) ∈ g} for each ς ∈ ϱ, defines a soft generalized topology on Ω.…”

Section: It Is Denoted Bymentioning

confidence: 99%

Section: Bs G-limit Points In Bsgt Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Bipolar Soft Limit Points in Bipolar Soft Generalized Topological Spaces

Saleh¹,

Asaad²,

Mohammed³

2022

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Economic Decision-Making Using Rough Topological Structures

El-Gayar

Abu-Gdairi

El-Bably

et al. 2023

Journal of Mathematics

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This paper suggests new approximations that are inspired by topological structures. The primary goal of this work is to define four neighborhoods resulting from a binary relation. Thus, we have four distinct techniques for approximating rough sets. The suggested approaches represent topological generalizations of the previous works. The characteristics and connections of these approaches are investigated. For the sake of the application, we provide some useful examples to compare our techniques to those in the published literature. The merit of the current technique is to obtain a more accurate decision for the problems in which these cases are the appropriate frame to describe them; for instance, machine learning (ML, for short) applications of finance, etc. To demonstrate this fact, an economic application is proposed. We employ the proposed technique in defining accurate decisions to identify the growth of countries. An algorithm for decision-making problems is proposed and tested on fictitious data to compare our methods with the previous approaches.

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Connectedness, local connectedness, and components on bipolar soft generalized topological spaces

Saleh¹,

Asaad²,

Mohammed³

2023

J. Math. Computer Sci.

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Connectedness represents the most significant and fundamental topological property. It highlights the main characteristics of topological spaces and distinguishes one topology from another. There is a constant study of bipolar soft generalized topological spaces (BSGTSs) by presenting BS g-connected set and BS g-connected space in BSGTSs as well as it is discussing some properties and results for these topics. Additionally, the notion of bipolar soft disjoint sets is put forward, BS g-separation set, g-separated BSSs and BS g-hereditary property. Moreover, there is an extensive study of BS g-locally connected space and BS g-component with some related properties and theorems following them, such as the concepts of BS g-locally connected spaces and BS g-connected are independent of each other; also determined the conditions under which the BS g-connected subsets are BS g-components.

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Bipolar Soft Generalized Topological Structures and Their Application in Decision Making

Cited by 5 publications

References 19 publications

Bipolar Soft Limit Points in Bipolar Soft Generalized Topological Spaces

Bipolar Soft Limit Points in Bipolar Soft Generalized Topological Spaces

Economic Decision-Making Using Rough Topological Structures

Connectedness, local connectedness, and components on bipolar soft generalized topological spaces

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