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.

scholarly journals A Tychonoff theorem in intuitionistic fuzzy topological spaces

2004 ◽  
Vol 2004 (70) ◽  
pp. 3829-3837
Author(s):  
Doğan Çoker ◽  
A. Haydar Eş ◽  
Necla Turanli
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff-like theorem.

scholarly journals Bipolar Soft Topological Spaces

2020 ◽  
Vol 13 (2) ◽  
pp. 227-245
Author(s):  
Asmaa Fadel ◽  
Syahida Che Dzul-Kifli
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
The Other ◽  
Topological Spaces ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Positive Information ◽  
Soft Limit ◽  
Soft Point ◽  
Soft Topological Space

Bipolar soft set theory is a mathematical tool associates between bipolarity and soft set theory, it is defined by two soft sets one of them gives us the positive information where the other gives us the negative. The goal of our paper is to define the bipolar soft topological space on a bipolar soft set and study its basic notions and properties. We also investigate the definitions of: bipolar soft interior, bipolar soft closure, bipolar soft exterior, bipolar soft boundary and establish some important properties on them. Some relations between them are also discussed. Moreover, the notions of bipolar soft point, bipolar soft limit point and the derived set of a bipolar soft set are discussed. In additions, examples are presented to illustrate our work.

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 New Soft Structure: Infra Soft Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Closure Operators ◽  
Relative Topology ◽  
Closed Sets ◽  
Soft Topology ◽  
Soft Limit ◽  
Basic Concepts ◽  
Soft Topological Space

It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

On pythagorean fuzzy soft topological spaces

2021 ◽  
pp. 1-9
Author(s):  
Ibtesam Alshammari ◽  
Mani Parimala ◽  
Saeid Jafari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Decision Making Process ◽  
Soft Sets ◽  
New Methods ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Fuzzy Soft Sets

Imprecision in the decision-making process is an essential consideration. In order to navigate the imprecise decision-making framework, measuring tools and methods have been developed. Pythagorean fuzzy soft sets are one of the new methods for dealing with imprecision. Pythagorean fuzzy soft topological spaces is an extension of intuitionistic fuzzy soft topological spaces. These sets generalizes intuitionistic fuzzy sets for a broader variety of implementations. This work is a gateway to study such a problem. The concept of Pythagorean fuzzy soft topological spaces(PyFSTS), interior, closure, boundary, neighborhood of Pythagorean fuzzy soft spaces PyFSS, base and subspace of PyFSTSs are presented and its properties are figured out. We established an algorithm under uncertainty based on PyFSTS for multi-attribute decision-making (MADM) and to validate this algorithm, a numerical example is solved for suitable brand selection. Finally, the benefits, validity, versatility and comparison of our proposed algorithms with current techniques are discussed.The advantage of the proposed work is to detect vagueness with more sizably voluminous valuation space than intuitionistic fuzzy sets.

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.

scholarly journals Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

2021 ◽  
Vol 7 (3) ◽  
pp. 3866-3895
Author(s):  
Atiqe Ur Rahman ◽  
◽  
Muhammad Saeed ◽  
Hamiden Abd El-Wahed Khalifa ◽  
Walaa Abdullah Afifi ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Approximate Function

<abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>

γ-Operation and Some Types of Soft Sets and Soft Continuity of (Supra) Soft Topological Spaces

2016 ◽  
pp. 127-171
Author(s):  
Ali Kandil ◽  
Osama A. El-Tantawy ◽  
Sobhy A. El-Sheikh ◽  
A. M. Abd El-latif
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Topological Properties ◽  
Soft Sets ◽  
Soft Mapping ◽  
Separation Axioms ◽  
Different Types

The main purpose of this chapter is to introduce the notions of ?-operation, pre-open soft set a-open sets, semi open soft set and ß-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces. We introduce new soft separation axioms based on the semi open soft sets which are more general than of the open soft sets. We show that the properties of soft semi Ti-spaces (i=1,2) are soft topological properties under the bijection and irresolute open soft mapping. Also, we introduce the notion of supra soft topological spaces. Moreover, we introduce the concept of supra generalized closed soft sets (supra g-closed soft for short) in a supra topological space (X,µ,E) and study their properties in detail.

On m-polar Diophantine fuzzy N-soft set with applications

2020 ◽  
Vol 23 ◽  
Author(s):  
Jia-Bao Liu ◽  
Shahbaz Ali ◽  
Muhammad Khalid Mahmood ◽  
Muhammad Haris Mateen
Keyword(s):  
Fuzzy Sets ◽  
Hybrid Model ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Proposed Model ◽  
Fuzzy Soft Sets ◽  
Novel Concept ◽  
Intuitionistic Fuzzy Soft Sets

Introduction: In this paper, we present a novel hybrid model m-polar Diophantine fuzzy N-soft set and define operations on it. Methods: We generalize the concepts of fuzzy sets, soft sets, N-soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets and Pythagorean fuzzy N-soft sets by incorporating our proposed model. Additionally, we define three different sorts of complements for Pythagorean fuzzy Nsoft sets and examine few outcomes which do not hold in Pythagorean fuzzy N-soft sets complements unlike to crisp set. We further discuss about (α, β, γ) -cut of m-polar Diophantine fuzzy N-soft sets and their properties. Lastly, we prove our claim that the defined model is a generalization of soft set, N-soft set, fuzzy N-soft set, intuitionistic fuzzy N soft set and Pythagorean fuzzy N-soft set. Results: m-polar Diophantine fuzzy N-soft set is more efficient and an adaptable model to manage uncertainties as it also overcome drawbacks of existing models which are to be generalized. Conclusion: We introduced novel concept of m-polar Diophantine fuzzy N-soft sets (MPDFNS sets).

Sign in / Sign up

Export Citation Format

Share Document