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.

α -CONNECTEDNESS BETWEEN SOFT SETS

2019 ◽  
Vol 7 (4) ◽  
pp. 09-14
Author(s):  
Alpa Singh Rajput ◽  
S. S. Thakur
Keyword(s):  
Image Processing ◽  
Image Segmentation ◽  
Topological Space ◽  
Topological Spaces ◽  
Soft Sets ◽  
Soft Topology ◽  
Feasible Path ◽  
Soft Topological Space

Purpose of the study: In the present paper the concept of soft α -connectedness between soft sets in soft topological spaces has been introduced and studied. The notion of connectedness captures the idea of hanging-togetherness of image elements in an object by given a firmness of connectedness to every feasible path between every possible pair of image elements. It is an important tool for the designing of algorithms for image segmentation. The purpose of this paper is to extend the concept of α –connectedness between sets in soft topology. Main Findings: If a soft topological space (X, τ, E) is soft α -connected between a pair of its soft sets, then it is not necessarily that it is soft α -connected between each pair of its soft sets and so it is not necessarily soft α -connected. Applications of this study: Image Processing. Novelty/Originality of this study: Extend of α -connectedness between soft sets in soft topology.

scholarly journals On Two Classes of Soft Sets in Soft Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 265 ◽  
Author(s):  
Samer Al Ghour ◽  
Worood Hamed
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Logical Connective ◽  
Soft Sets ◽  
Natural Properties ◽  
Soft Topological Space

In this paper, we define soft ω -open sets and strongly soft ω -open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological spaces. Also, we study the relationships between the ω -open sets of a given indexed family of topological spaces and the soft ω -open sets (resp. strongly soft ω -open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω -open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.

scholarly journals On Soft Topological Space via Semiopen and Semiclosed Soft Sets

2014 ◽  
Vol 54 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Juthika Mahanta ◽  
Pramod Kumar Das
Keyword(s):  
Topological Space ◽  
Soft Sets ◽  
Soft Topological Space

scholarly journals On *Soft Turing Point with Separation Axioms

2018 ◽  
Vol 26 (7) ◽  
pp. 200-209
Author(s):  
Ahmed B. AL-Nafee
Keyword(s):  
Topological Space ◽  
Separation Axioms ◽  
The Relationship ◽  
Soft Topological Space

  " In this paper, we use the concept of the soft turing point and join it with separation axioms in soft topological space and investigate the relationship between them and  study the most important properties and  results of it.  

scholarly journals A Review of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces and Neutrosophic Soft Topological Spaces

2020 ◽  
pp. 96-104
Author(s):  
admin admin ◽  
◽  
◽  
◽  
M M.Karthika ◽  
...  
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Topological Structure ◽  
Intuitionistic Fuzzy Set ◽  
Soft Set ◽  
Topological Spaces ◽  
Soft Sets ◽  
Structure Space ◽  
Intuitionistic Fuzzy ◽  
Soft Topological Space

The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, in- tuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review of soft topological spaces in various sets like fuzzy, Intuitionistic fuzzy set and neutrosophy. Eventually, we compared some of the existing tools in the literature for easy understanding and exhibited their advantages and limitations.

Bipolar neutrosophic soft generalized pre-continuous mappings

2021 ◽  
pp. 101-110
Author(s):  
Arulpandy P ◽  
◽  
◽  
Trinita Pricilla M
Keyword(s):  
Topological Space ◽  
Soft Sets ◽  
Topological Structures ◽  
Continuous Mappings ◽  
Soft Topological Space

In this study, new classes of continuous mappings in bipolar neutrosophic soft topological space, namely bipolar neutrosophic soft continuous mappings and bipolar neutrosophic soft generalized pre-continuous mappings has been introduced. Continuity mappings preserves topological structures such as closeness, openness, compactness and so on. Here, we have proposed and investigated various continuous mappings based on bipolar neutrosophic soft sets. Further, we investigated some of their properties and relations with other mappings with examples.

scholarly journals On Soft Semi Weakly Generalized Closed Set in Soft TopologicalSpaces

2019 ◽  
Vol 8 (12) ◽  
pp. 1252-1256 ◽  
Keyword(s):  
Social Science ◽  
Topological Space ◽  
Life Science ◽  
Soft Sets ◽  
Science And Engineering ◽  
Closed Set ◽  
Soft Topology ◽  
Soft Topological Space

Soft sets has helped the development of soft topological space and it was also applied in the field of life science, Social science and Engineering. Many researchers developed various ideas based on the properties of soft topology. The article deals with study of properties in soft topological space based on soft semi weakly generalized closed set

C̆ech Fuzzy Soft Closure Spaces

2018 ◽  
Vol 7 (2) ◽  
pp. 62-74 ◽  
Author(s):  
Rasha Naser Majeed
Keyword(s):  
Topological Space ◽  
Subject Classification ◽  
Closure Space ◽  
Soft Sets ◽  
Basic Properties ◽  
Closed Mapping ◽  
Closure Spaces ◽  
Fuzzy Soft Sets ◽  
Soft Topological Space

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

New concepts on the structure of the neuronal networks: The miniaturization and hierarchical organization of the central nervous system*

1984 ◽  
Vol 4 (2) ◽  
pp. 93-98 ◽  
Author(s):  
Luigi F. Agnati ◽  
Kjell Fuxe
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Neuronal Networks ◽  
Hierarchical Organization ◽  
Memory Storage ◽  
Information Handling ◽  
New Concepts ◽  
The Central Nervous System ◽  
Local Circuits ◽  
The Relationship

The hypothesis is introduced that miniaturization of neuronal circuits in the central nervous system and the hierarchical organization of the various levels, where information handling can take place, may be the key to understand the enormous capability of the human brain to store engrams as well as its astonishing capacity to reconstruct and organize engrams and thus to perform highly sophisticated integrations. The concept is also proposed that in order to understand the relationship between the structural and functional plasticity of the central nervous system it is necessary to postulate the existence of memory storage at the network level, at the local circuit level, at the synaptic level, at the membrane level, and finally at the molecular level. Thus, memory organization is similar to the hierarchical organization of the various levels, where information handling takes place in the nervous system. In addition, each higher level plays a role in the reconstruction and organization of the engrams stored at lower levels. Thus, the trace of the functionally stored memory (i.e. its reconstruction and organization at various levels of storage) will depend not only on the chemicophysical changes in the membranes of the local circuits but also on the organization of the local circuits themselves and their associated neuronal networks.

Fear, history, stigma, and bias in the COVID-19 pandemic

2020 ◽  
Vol 18 (7) ◽  
pp. 177-182
Author(s):  
Kevin Kupietz, PhD ◽  
Lesley Gray, MPH
Keyword(s):  
Emergency Management ◽  
Disease Outbreaks ◽  
Social Effects ◽  
Evidence Based ◽  
Stigma And Discrimination ◽  
Emergency Managers ◽  
Global Pandemic ◽  
New Concepts ◽  
History Of ◽  
The Relationship

Introduction: The greatest enemy of a global pandemic is not the virus itself, but the fear, rumor, and stigma that envelopes people. This article explores the context and history of fear and stigma relating to pandemic, summarizing key actions to mitigate the harms during an active pandemic.Method: Our article draws from accounts in literature and journalist accounts documenting the relationship between infectious diseases and major disease outbreaks that have garnered fear and stigmatization. Results: Fear, stigma, and discrimination are not new concepts for pandemics. These social effects run the risk of diverting attention from the presenting disease and government responses. Reactions to fear, stigma, and discrimination risk sabotaging effective efforts to contain, manage, and eradicate the disease.Conclusion: Emergency managers have an important role in dispelling myths, disseminating appropriate and evidence-based information without exacerbating fears. Knowledge about the roots of fear and bias along with a good understanding of historical plagues and pandemics is vital to ensure those in the field of emergency management can effectively manage irrational fears.

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