Some results on soft element and soft topological space

Polat, Nazan Çakmak; Yaylalı, Gözde; Tanay, Bekir

doi:10.1002/mma.5778

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…One of them is Wardowski [13] who defined soft element which provides soft topological structures resembles to pointwise topological structures. After this definition there have been studies on soft topological and soft algebraic structures from an elementary point of view such as [14] and [15] etc.…”

Section: Introductionmentioning

confidence: 99%

On Soft Ring and Soft Topological Ring

POLAT,

YAYLALI UMUL,

TANAY

2023

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

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Soft set theory is an affective mathematical tool to solve problems that involves uncertainties. Despite the development in the theoretical structure of soft sets, researchers did not make consensus formulation of soft element. In this study soft ring is redefined by the help of soft operation which are based on a natural definition of soft element. This new soft ring definition is compared with the soft ring definition in the literature. Some examples, results and theorems are given to enrich the concept of soft ring. Also soft topological ring structure which is a harmonization of soft ring and soft topology is studied with some results.

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Section: Introductionmentioning

confidence: 99%

On Soft Ring and Soft Topological Ring

POLAT,

YAYLALI UMUL,

TANAY

2023

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

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“…Taşköprü and Altıntaş [27] researched a soft topology and soft function via soft element. Polat et al [28] also worked on soft topology. Soft set theory has a wide place in decision-making, as it does in every field.…”

Section: Introductionmentioning

confidence: 99%

Application of soft ideals to two new types: the soft primary ideal and the soft 1-absorbing primary ideal

Çıtak

KANAT

2023

Preprint

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In this paper, we introduce two new types of ideals. The first of these is a soft primary ideal, a generalization of the soft prime ideal. We work theoretically and practically in the first part on this new concept. One of the most important results we have achieved is that the concept of a soft primary ideal is a generalization of a soft prime ideal. Namely, a soft prime ideal is a soft primary ideal, but a primary ideal does not need to be a prime ideal. Another important result is that the radical of a soft primary ideal is a soft prime ideal. In addition, with the help of a soft primary ideal, we obtain a primary ideal of the ring under suitable conditions. In the second part, we describe and examine the concept of a soft 1-absorbing primary ideal, a generalization of the soft primary ideal. In this part, we show that every soft primary ideal is a 1-absorbing primary ideal, but the reverse of this situation is not valid. The soft 1-absorbing primary ideal also is a generalization of the soft prime ideal. In this section, we have proved that the radical of the soft 1-absorbing primary ideal is the soft prime ideal. Finally, we determine that algebraic features of soft primary ideal and soft 1-absorbing primary ideal are guarded under ring homomorphisms.

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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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Some results on soft element and soft topological space

Cited by 5 publications

References 12 publications

On Soft Ring and Soft Topological Ring

On Soft Ring and Soft Topological Ring

Application of soft ideals to two new types: the soft primary ideal and the soft 1-absorbing primary ideal

Topological Structures via Bipolar Hypersoft Sets

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