A Link between Topology and Soft Topology

Kiruthika, Marimuthu; Thangavelu, P.

doi:10.15672/hjms.2018.551

Cited by 5 publications

(5 citation statements)

References 8 publications

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“…Çaǧman et al [10] used a soft set to demonstrate the notion of soft topological space. Following that, several academics concentrated on soft topological spaces [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

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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Section: Introductionmentioning

confidence: 99%

Topological Structures via Bipolar Hypersoft Sets

Musa

Asaad

2022

Journal of Mathematics

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“…e notion of Pythagorean fuzzy topological space was presented by Olgun et al [34]. Kiruthika and angavelu [35] discussed the link between topology and soft topology. Recently, by using elementary operations over a universal set with a set of parameters, Taskopru and Altintas [36] established the elementary soft topology.…”

Section: Introductionmentioning

confidence: 99%

Spherical Fuzzy Soft Topology and Its Application in Group Decision-Making Problems

Garg

John

et al. 2022

Mathematical Problems in Engineering

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The spherical fuzzy soft set is a generalized soft set model, which is more realistic, practical, and accurate. It is an extended version of existing fuzzy soft set models that can be used to describe imprecise data in real-world scenarios. The paper seeks to introduce the new concept of spherical fuzzy soft topology defined on spherical fuzzy soft sets. In this work, we define some basic concepts including spherical fuzzy soft basis, spherical fuzzy soft subspace, spherical fuzzy soft interior, spherical fuzzy soft closure, and spherical fuzzy soft boundary. The properties of these defined set are also discussed and explained with an appropriate examples. Also, we establish certain important results and introduce spherical fuzzy soft separation axioms, spherical fuzzy soft regular space, and spherical fuzzy soft normal space. Furthermore, as an application, a group decision-making algorithm is presented based on the TOPSIS (Technique of Order Preference by Similarity to an Ideal Solution) method for solving the decision-making problems. The applicability of the proposed method is demonstrated through a numerical example. The comprehensive advantages of the proposed work have been stated over the existing methods.

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“…Olgun et al [51], introduced the concept of Pythagorean fuzzy topological space. Topology and soft topology were addressed by Kiruthika and Thangavelu [52]. Dizman and Ozturk [53] defined fuzzy bipolar soft topological spaces.…”

Section: Introductionmentioning

confidence: 99%

Bipolar Spherical Fuzzy Soft Topology with Applications to Multi-Criteria Group Decision-Making in Buildings Risk Assessment

Yolcu

2022

Symmetry

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A generalized soft set model that is more accurate, useful, and realistic is the bipolar spherical fuzzy soft set (BSFSs). It is a more developed variant of current fuzzy soft set models that may be applied to characterize erroneous data in practical applications. Bipolar spherical fuzzy soft sets and bipolar spherical fuzzy soft topology are novel ideas that are intended to be introduced in this work. Bipolar spherical fuzzy soft intersection, bipolar spherical fuzzy soft null set, spherical fuzzy soft absolute set, and other operations on bipolar spherical fuzzy soft sets are some of the fundamental ideas defined in this work. The bipolar spherical fuzzy soft open set, the bipolar spherical fuzzy soft close set, the bipolar spherical fuzzy soft closure, and the spherical fuzzy soft interior are also defined. Additionally, the characteristics of this specified set are covered and described using pertinent instances. The innovative notion of BSFSs makes it easier to describe the symmetry of two or more objects. Moreover, a group decision-making algorithm based on the TOPSIS (Technique of Order Preference by Similarity to an Ideal Solution) approach to problem-solving is described. We analyze the symmetry of the optimal decision and ranking of feasible alternatives. A numerical example is used to show how the suggested approach may be used. The extensive benefits of the proposed work over the existing techniques have been listed.

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A Link between Topology and Soft Topology

Abstract: Muhammad Shabir and Munazza Naz have shown that every soft topology gives a parametrized family of topologies on a set X. In this paper such a link between topology and soft topology is further discussed.

Cited by 5 publications

References 8 publications

Topological Structures via Bipolar Hypersoft Sets

Topological Structures via Bipolar Hypersoft Sets

Spherical Fuzzy Soft Topology and Its Application in Group Decision-Making Problems

Bipolar Spherical Fuzzy Soft Topology with Applications to Multi-Criteria Group Decision-Making in Buildings Risk Assessment

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