scholarly journals Infra Soft Semiopen Sets and Infra Soft Semicontinuity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Tareq M. Al-shami ◽  
A. A. Azzam
Keyword(s):  
Soft Set ◽  
Finite Product ◽  
Finite Intersection ◽  
Soft Topology ◽  
Continuous Mappings

To contribute to the area of infra soft topology, we introduce one of the generalizations of infra soft open sets called infra soft semiopen sets. We establish some characterizations of them and study their main properties. We determine under what condition this class is closed under finite intersection and show that this class is preserved under infra soft continuous mappings and finite product of soft spaces. Then, we present the concepts of infra semi-interior, infra semiclosure, infra semilimit, and infra semiboundary soft points of a soft set and elucidate the relationships between them. Finally, we exploit infra soft semiopen and infra soft semiclosed sets to define new types of soft mappings. We characterize each one of these soft mappings and explore main features.

scholarly journals Infra Soft Compact Spaces and Application to Fixed Point Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Topological Properties ◽  
Finite Product ◽  
Finite Intersection ◽  
Compact Spaces ◽  
Closed Sets ◽  
Soft Topology ◽  
Covering Properties

Infra soft topology is one of the recent generalizations of soft topology which is closed under finite intersection. Herein, we contribute to this structure by presenting two kinds of soft covering properties, namely, infra soft compact and infra soft Lindelöf spaces. We describe them using a family of infra soft closed sets and display their main properties. With the assistance of examples, we mention some classical topological properties that are invalid in the frame of infra soft topology and determine under which condition they are valid. We focus on studying the “transmission” of these concepts between infra soft topology and classical infra topology which helps us to discover the behaviours of these concepts in infra soft topology using their counterparts in classical infra topology and vice versa. Among the obtained results, these concepts are closed under infra soft homeomorphisms and finite product of soft spaces. Finally, we introduce the concept of fixed soft points and reveal main characterizations, especially those induced from infra soft compact spaces.

scholarly journals Soft ditopological spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 209-222 ◽  
Author(s):  
Tugbahan Dizman ◽  
Alexander Sostak ◽  
Saziye Yuksel
Keyword(s):  
Fuzzy Sets ◽  
Soft Set ◽  
Fuzzy Topology ◽  
Basic Properties ◽  
Soft Topology ◽  
Continuous Mappings ◽  
Basic Concepts

We introduce the concept of a soft ditopological space as the "soft Generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Ert?rk, ?. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 171-199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.

Connectedness Between Soft Sets

2018 ◽  
Vol 14 (01) ◽  
pp. 53-71 ◽  
Author(s):  
Samajh Singh Thakur ◽  
Alpa Singh Rajput
Keyword(s):  
Soft Set ◽  
Topological Spaces ◽  
Soft Sets ◽  
Continuous Mappings ◽  
Weakly Continuous

In the present paper, the concepts of soft connectedness between soft sets, soft set-connected and soft weakly continuous mappings in soft topological spaces have been introduced and studied.

scholarly journals Neutrosophic soft δ-topology and neutrosophic soft δ-compactness

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3441-3458
Author(s):  
Ahu Acikgoz ◽  
Ferhat Esenbel
Keyword(s):  
Basic Properties ◽  
Soft Topology ◽  
Open Set ◽  
Continuous Mappings ◽  
Regular Open

We introduce the concepts of neutrosophic soft ?-interior, neutrosophic soft quasi-coincidence, neutrosophic soft q-neighbourhood, neutrosophic soft regular open set, neutrosophic soft ?-closure, neutrosophic soft ?-closure and neutrosophic soft semi open set. It is also shown that the set of all neutrosophic soft ?-open sets is a neutrosophic soft topology, which is called the neutrosophic soft ?-topology. We obtain equivalent forms of neutrosophic soft ?-continuity. Moreover, the notions of neutrosophic soft ?-compactness and neutrosophic soft locally ?-compactness are defined and their basic properties under neutrosophic soft ?-continuous mappings are investigated.

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.

scholarly journals SOFT ALMOST β-CONTINUITY IN SOFT TOPOLOGICAL SPACES

2020 ◽  
Vol 8 (2) ◽  
pp. 06-14
Author(s):  
Alpa Singh Rajput ◽  
S. S. Thakur ◽  
Om Prakash Dubey
Keyword(s):  
Image Segmentation ◽  
Information Systems ◽  
Mathematical Models ◽  
General Framework ◽  
Continuous Mapping ◽  
Topological Spaces ◽  
Major Area ◽  
Soft Topology ◽  
Continuous Mappings

Purpose: In the present paper the concept of soft almost β-continuous mappings and soft almost β-open mappings in soft topological spaces have been introduced and studied. Methodology: This notion is weaker than both soft almost pre-continuous mappings, soft almost semi-continuous mapping. The diagrams of implication among these soft classes of soft mappings have been established. Main Findings: We extend the concept of almost β-continuous mappings and almost β-open mappings in soft topology. Implications: Mapping is an important and major area of topology and it can give many relationships between other scientific areas and mathematical models. This notion captures the idea of hanging-togetherness of image elements in an object by assigning strength of connectedness to every possible path between every possible pair of image elements. It is an important tool for the designing of algorithms for image segmentation. The novelty of Study: Hope that the concepts and results established in this paper will help the researcher to enhance and promote the further study on soft topology to carry out a general framework for the development of information systems.

scholarly journals Compactness on Soft Topological Ordered Spaces and Its Application on the Information System

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
T. M. Al-shami
Keyword(s):  
Information System ◽  
Missing Values ◽  
Product Spaces ◽  
Finite Product ◽  
Soft Sets ◽  
Finite Intersection ◽  
Compact Spaces ◽  
Ordered Space ◽  
Finite Spaces ◽  
Soft Topological Space

It is well known every soft topological space induced from soft information system is soft compact. In this study, we integrate between soft compactness and partially ordered set to introduce new types of soft compactness on the finite spaces and investigate their application on the information system. First, we initiate a notion of monotonic soft sets and establish its main properties. Second, we introduce the concepts of monotonic soft compact and ordered soft compact spaces and show the relationships between them with the help of examples. We give a complete description for each one of them by making use of the finite intersection property. Also, we study some properties associated with some soft ordered spaces and finite product spaces. Furthermore, we investigate the conditions under which these concepts are preserved between the soft topological ordered space and its parametric topological ordered spaces. In the end, we provide an algorithm for expecting the missing values of objects on the information system depending on the concept of ordered soft compact spaces.

scholarly journals Signal Soft Sets for Atoms Modeling and Signal Soft Topology

2021 ◽  
pp. 269-274
Author(s):  
Majd Hamid Mahmood
Keyword(s):  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Soft Topology

In this paper we define a signal soft set as a mathematical tool to represent and study atoms, anti-atoms, electrons, anti-electrons, protons, and anti-protons, and generate a signal soft topology, with an example of signal soft topology on H2O.

scholarly journals Some Properties of Soft β-Connected Spaces in Soft Topological Spaces

2017 ◽  
Vol 18 ◽  
pp. 13-21
Author(s):  
S.S. Benchalli ◽  
Prakash Gouda Patil ◽  
Abeda S. Dodamani
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Theory And Practice ◽  
Topological Spaces ◽  
Soft Topology ◽  
Practical Life ◽  
Connected Spaces

Soft set theory is a newly emerging tool to deal with uncertain problems and has been studied by researchers in theory and practice. In this paper, we investigated the properties and characterizations of softβ-connected spaces in soft topological spaces. We anticipate that the results in this paper can be stimulated to the further study on soft topology to accomplish genenral framework for the practical life applications.

Multi-criteria group decision making with Pythagorean fuzzy soft topology

2020 ◽  
Vol 39 (5) ◽  
pp. 6703-6720
Author(s):  
Muhammad Riaz ◽  
Khalid Naeem ◽  
Muhammad Aslam ◽  
Deeba Afzal ◽  
Fuad Ali Ahmed Almahdi ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Real World ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Pythagorean Fuzzy Set ◽  
Soft Topology

Pythagorean fuzzy set (PFS) introduced by Yager (2013) is the extension of intuitionistic fuzzy set (IFS) introduced by Atanassov (1983). PFS is also known as IFS of type-2. Pythagorean fuzzy soft set (PFSS), introduced by Peng et al. (2015) and later studied by Guleria and Bajaj (2019) and Naeem et al. (2019), are very helpful in representing vague information that occurs in real world circumstances. In this article, we introduce the notion of Pythagorean fuzzy soft topology (PFS-topology) defined on Pythagorean fuzzy soft set (PFSS). We define PFS-basis, PFS-subspace, PFS-interior, PFS-closure and boundary of PFSS. We introduce Pythagorean fuzzy soft separation axioms, Pythagorean fuzzy soft regular and normal spaces. Furthermore, we present an application of PFSSs to multiple criteria group decision making (MCGDM) using choice value method in the real world problems which yields the optimum results for investment in the stock exchange. We also render an application of PFS-topology in medical diagnosis using TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). The applications are accompanied by Algorithms, flow charts and statistical diagrams.

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