Bipolar Soft Topological Spaces

Fadel, Asmaa; Dzul-Kifli, Syahida Che

doi:10.29020/nybg.ejpam.v13i2.3645

Cited by 12 publications

(10 citation statements)

References 12 publications

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“…Definition 13. [20] The bipolar soft difference between two bipolar soft sets (Θ 1 , Λ 1 , ς) and (Θ 2 , Λ 2 , σ) is the bipolar soft set (Θ, Λ, κ) where κ = ς ∪ σ is defined as…”

Section: It Is Denoted Bymentioning

confidence: 99%

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Bipolar Soft Generalized Topological Structures and Their Application in Decision Making

Saleh

Asaad²,

Mohammed

2022

Eur. J. Pure Appl. Math.

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The basic of bipolar soft set theory stands for a mathematical instrument that bringstogether the soft set theory and bipolarity. Its definition is based on two soft sets, a set thatprovides positive information and other that gives negative. This paper mainly aims at defininga new bipolar soft generalized topological space; setting out of the point that the collection ofbipolar soft sets forms the basis for the definition of the new concept is defined. Added to that,an investigation has been made of the four concepts of bipolar soft generalized, namely g-interior,g-closure, g-exterior and g-boundary. Furthermore, the main properties of bipolar soft generalizedtopological space (BSGT S) are established. This paper also attends to the discussion of therelations between these new definitions and the application of the given bipolar soft generalizedtopological spaces in a decision-making problem where an algorithm for this application has beensuggested. Finally, to clarify and substantiate what the current work subsumes, some exampleshave been provided.

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Section: It Is Denoted Bymentioning

confidence: 99%

“…There has been an expansion of the definition of bipolar soft topological spaces defined in [36] by Fadel and Dzul-Kifli [20] who have attended to the key concepts and properties and put forward some illustrative examples. Additionally, there has been further works on the topological structures on bipolar soft sets, (see [21], [22]).…”

Section: Introductionmentioning

confidence: 99%

Bipolar Soft Generalized Topological Structures and Their Application in Decision Making

Saleh

Asaad²,

Mohammed

2022

Eur. J. Pure Appl. Math.

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“…e notions of interior and closure operators, basis, and subspace in bipolar soft topological spaces were studied by Ozturk [34]. By redefining bipolar soft topological spaces on a bipolar soft set, Fadel [35] has expanded the definition of bipolar soft topological spaces introduced in [33]. ey have covered the key concepts and properties, as well as some illustrative examples.…”

Section: Introductionmentioning

confidence: 99%

Topological Structures via Bipolar Hypersoft Sets

Musa

Asaad

2022

Journal of Mathematics

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In this article, we introduce bipolar hypersoft topological spaces over the collection of bipolar hypersoft sets. It is proven that a bipolar hypersoft topological space gives a parametrized family of hypersoft topological spaces, but the converse does not hold in general, and this is shown with the help of an example. Furthermore, we give a condition on a given parametrized family of hypersoft topologies, which assure that there is a bipolar hypersoft topology whose induced family of hypersoft topologies is the given family. The notions of bipolar hypersoft neighborhood, bipolar hypersoft subspace, and bipolar hypersoft limit points are introduced. Finally, we define bipolar hypersoft interior, bipolar hypersoft closure, bipolar hypersoft exterior, and bipolar hypersoft boundary, and the relations between them, differing from the relations on hypersoft topology, are investigated.

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“…Fadel and Hassan [30] presented the concepts of bipolar soft separation axioms and established fundamental properties. Recently, Fadel and Dzul-Kifli [31] have generalized the concept of bipolar soft topological spaces given in [28] by redefining it on a bipolar soft set. ey have presented its main notions and described properties along with some illustrative examples.…”

Section: Introductionmentioning

confidence: 99%

Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications

Al-shami

2021

Complexity

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Bipolar soft set is formulated by two soft sets; one of them provides us the positive information and the other provides us the negative information. The philosophy of bipolarity is that human judgment is based on two sides, positive and negative, and we choose the one which is stronger. In this paper, we introduce novel belong and nonbelong relations between a bipolar soft set and an ordinary point. These relations are considered as one of the unique characteristics of bipolar soft sets which are somewhat expression of the degrees of membership and nonmembership of an element. We discuss essential properties and derive the sufficient conditions of some equivalence of these relations. We also define the concept of soft mappings between two classes of bipolar soft sets and study the behaviors of an ordinary point under these soft mappings with respect to all relations introduced herein. Then, we apply bipolar soft sets to build an optimal choice application. We give an algorithm of this application and show the method for implementing this algorithm by an illustrative example. In conclusion, it can be noted that the relations defined herein give another viewpoint to explore the concepts of bipolar soft topology, in particular, soft separation axioms and soft covers.

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Bipolar Soft Topological Spaces

Cited by 12 publications

References 12 publications

Bipolar Soft Generalized Topological Structures and Their Application in Decision Making

Bipolar Soft Generalized Topological Structures and Their Application in Decision Making

Topological Structures via Bipolar Hypersoft Sets

Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications

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