scholarly journals An Absolutely New Attempt to Vague Soft Bitopological Spaces Basis at Newly Defined Operations regarding Vague Soft Points

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Arif Mehmood ◽  
Farkhanda Afzal ◽  
Saleem Abdullah ◽  
Muhammad Imran Khan ◽  
Saeed Gul
Keyword(s):  
Soft Sets ◽  
Closed Sets ◽  
Soft Topology ◽  
Separation Axioms ◽  
Bitopological Spaces

In this study, new operations of union, intersection, and complement are defined with the help of vague soft sets in a new way that is in both true and false statements, union is defined with maximum, and intersection is defined with minimum. On the basis of these operations, vague soft topology is defined. Pairwise vague soft open sets and pairwise vague soft closed sets are defined in vague soft bitopological structures (VSBTS). Moreover, generalized vague soft open sets are introduced in VSBTS concerning soft points of the space. On the basis of generalized vague soft open sets, separation axioms are also introduced. In continuation, these separations axioms are engaged with other important results in VSBTS.

scholarly journals Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tareq M. Al-shami ◽  
Abdelwaheb Mhemdi
Keyword(s):  
Soft Sets ◽  
Soft Topology ◽  
Educational Application ◽  
Separation Axioms ◽  
Different Types ◽  
Ordinary Point ◽  
The Relationship

We aim through this paper to achieve two goals: first, we define some types of belong and nonbelong relations between ordinary points and double-framed soft sets. These relations are one of the distinguishing characteristics of double-framed soft sets and are somewhat expression of the degrees of membership and nonmembership. We explore their main properties and determine the conditions under which some of them are equivalent. Also, we introduce the concept of soft mappings between two classes of double-framed soft sets and investigate the relationship between an ordinary point and its image and preimage with respect to the different types of belong and nonbelong relations. By the notions presented herein, many concepts can be studied on double-framed soft topology such as soft separation axioms and cover properties. Second, we give an educational application of optimal choices using the idea of double-framed soft sets. We provide an algorithm of this application with an example to show how this algorithm is carried out.

Soft sets and soft topology on nearness approximation spaces

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4117-4125 ◽  
Author(s):  
Hatice Tasbozan ◽  
Ilhan Icen ◽  
Nurettin Bagirmaz ◽  
Abdullah Ozcan
Keyword(s):  
Soft Sets ◽  
Approximation Spaces ◽  
Soft Topology

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

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1781
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Soft Sets ◽  
New Concepts ◽  
Bitopological Spaces ◽  
The Relationship ◽  
Soft Topological Space

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.

scholarly journals Generalized ψ∗-closed sets in bitopological spaces

2015 ◽  
Vol 23 (3) ◽  
pp. 527-534 ◽  
Author(s):  
H.M. Abu Donia ◽  
M.A. Abd Allah ◽  
A.S. Nawar
Keyword(s):  
Closed Sets ◽  
Bitopological Spaces

scholarly journals On Soft Turning Points

2018 ◽  
Vol 15 (3) ◽  
pp. 352-360
Author(s):  
Baghdad Science Journal
Keyword(s):  
Turning Points ◽  
Soft Sets ◽  
Great Flexibility ◽  
Separation Axioms ◽  
Soft Limit ◽  
Limit Points

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

scholarly journals On generalized γµ-closed sets and related continuity

2021 ◽  
Vol 13 (2) ◽  
pp. 483-493
Author(s):  
Ritu Sen
Keyword(s):  
Topological Space ◽  
Main Interest ◽  
Closed Sets ◽  
Separation Axioms ◽  
Preservation Theorems ◽  
Generalized Topological Space ◽  
New Type ◽  
Weak Separation

Abstract In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.

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