scholarly journals On Topological Structures of Fuzzy Parametrized Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Serkan Atmaca ◽  
İdris Zorlutuna
Keyword(s):  
Topological Structure ◽  
Topological Spaces ◽  
Soft Sets ◽  
Topological Structures ◽  
Basic Properties

We introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated its basic properties. We study the closure, interior, base, continuity, and compactness and properties of these concepts in fuzzy parametrized soft topological spaces.

scholarly journals Topological Structure of Vague Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chang Wang ◽  
Yaya Li
Keyword(s):  
Topological Structure ◽  
Topological Spaces ◽  
Soft Sets ◽  
Basic Properties ◽  
Closed Sets ◽  
Fixed Set

We introduce vague soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of vague soft open sets, vague soft closed sets, vague soft interior, vague soft closure, and vague soft boundary are introduced and their basic properties and relations are investigated. Furthermore, with the help of examples they established that some properties of topological spaces and soft topological spaces do not hold in vague soft topological spaces. Vague soft connectedness and vague soft compactness are also studied.

scholarly journals On topological structures of virtual fuzzy parametrized fuzzy soft sets

2021 ◽  
Author(s):  
Orhan Dalkiliç
Keyword(s):  
Mathematical Models ◽  
Set Theory ◽  
Topological Structure ◽  
Soft Set ◽  
Decision Makers ◽  
Topological Spaces ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Topological Structures ◽  
Fuzzy Soft Sets

AbstractWith the generalization of the concept of set, more comprehensive structures could be constructed in topological spaces. In this way, it is easier to express many relationships on existing mathematical models in a more comprehensive way. In this paper, the topological structure of virtual fuzzy parametrized fuzzy soft sets is analyzed by considering the virtual fuzzy parametrized fuzzy soft set theory, which is a hybrid set model that offers very practical approaches in expressing the membership degrees of decision makers, which has been introduced to the literature in recent years. Thus, it is aimed to contribute to the development of virtual fuzzy parametrized fuzzy soft set theory. To construct a topological structure on virtual fuzzy parametrized fuzzy soft sets, the concepts of point, quasi-coincident and mapping are first defined for this set theory and some of its characteristic properties are investigated. Then, virtual fuzzy parametrized fuzzy soft topological spaces are defined and concepts such as open, closed, closure, Q-neighborhood, interior, base, continuous, cover and compact are given. In addition, some related properties of these concepts are analyzed. Finally, many examples are given to make the paper easier to understand.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

ON Neutrosophic Crisp Supra Bi-Topological Spaces

2020 ◽  
pp. 36-46
Author(s):  
Riad K. Al Al-Hamido ◽  
Keyword(s):  
Topological Structure ◽  
General Structure ◽  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Open Set

In this paper, neutrosophic crisp supra bi-topological structure, which is a more general structure than neutrosophic crisp supra topological spaces, is built on neutrosophic crisp sets. The necessary arguments which are pairwise neutrosophic crisp supra open set, pairwise neutrosophic crisp supra closed set, pairwise neutrosophic crisp supra closure, pairwise neutrosophic crisp supra interior is defined, and their basic properties are presented. Finally, many examples are presented.

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.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

scholarly journals Topological Sensitivity in the Recognition of Disoriented Figures

i-Perception ◽  
2018 ◽  
Vol 9 (6) ◽  
pp. 204166951880971 ◽  
Author(s):  
Fumio Kanbe
Keyword(s):  
Structural Properties ◽  
Topological Structure ◽  
Topological Property ◽  
Topological Sensitivity ◽  
Topological Structures ◽  
Invariant Features

A previous study by the author found that discrimination latencies for figure pairs with the same topological structure (isomorphic pairs) were longer than for pairs with different topological structures (nonisomorphic pairs). These results suggest that topological sensitivity occurs during figure recognition. However, sameness was judged in terms of both shape and orientation. Using this criterion, faster discrimination of nonisomorphic pairs may have arisen from the detection of differences in the corresponding locations of the paired figures, which is not a topological property. The current study examined whether topological sensitivity occurs even when identity judgments are based on the sameness of shapes, irrespective of their orientation, where the sameness of location is not ensured. The current results suggested the involvement of topological sensitivity, indicating that processing of structural properties (invariant features) of a figure may be prioritized over processing of superficial features, such as location, length, and angles, in figure recognition.

Generalized μ(m,n)b-open and closed functions in bigeneralized topological spaces

2016 ◽  
Vol 09 (04) ◽  
pp. 1650076
Author(s):  
Methos Kristy Villar Donesa ◽  
Helen Moso Rara
Keyword(s):  
Topological Spaces ◽  
Basic Properties ◽  
Open Formula

The purpose of this paper is to introduce the notions of [Formula: see text]-open, [Formula: see text]-closed, quasi [Formula: see text]-open, and quasi [Formula: see text]-closed functions in bigeneralized topological spaces. Basic properties, characterizations and relationships between these functions are obtained.

scholarly journals On t-Neighbourhoods in Trigonometric Topological Spaces

2021 ◽  
Vol 12 (1S) ◽  
pp. 655-658
Author(s):  
S. Malathi, Et. al.
Keyword(s):  
Necessary Condition ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Type ◽  
The Relationship

In this paper we introduce a new type of neighbourhoods, namely, t-neighbourhoods in trigonometric topological spaces and study their basic properties. Also, we discuss the relationship between neighbourhoods and t-neighbourhoods. Further, we give the necessary condition for t-neighbourhoods in trigonometric topological spaces.  .

scholarly journals Supra Generalized Closed Soft Sets with Respect to an Soft Ideal in Supra Soft Topological Spaces

2014 ◽  
Vol 8 (4) ◽  
pp. 1731-1740 ◽  
Author(s):  
A. Kandil ◽  
O. A. E. Tantawy ◽  
S. A. El-Sheikh ◽  
A. M. Abd El-latif
Keyword(s):  
Topological Spaces ◽  
Soft Sets
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