scholarly journals Limit Points and Separation Axioms with Respect to Supra Semi-open Sets

2020 ◽  
Vol 13 (3) ◽  
pp. 427-443 ◽  
Author(s):  
Tareq M. AL-shami ◽  
E. A. Abo-Tabl ◽  
Baravan Assad ◽  
Mohamed Arahet
Keyword(s):  
Real Life ◽  
Research Area ◽  
Topological Spaces ◽  
Difference Property ◽  
Separation Axioms ◽  
Life Problems ◽  
New Concepts ◽  
Limit Points ◽  
The Difference

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between certain topological concepts, or preserving some properties under fewer conditions of those on topology. To contribute this research area, in this paper, we establish some new concepts on supra topological spaces using supra semi-open sets and give some characterizations of them. First, we introduce a concept of supra semi limit points of a set and study main properties, in particular, on the spaces that possess the difference property. Second, we define and investigate new separation axioms, namely supra semi Ti-spaces (i = 0, 1, 2, 3, 4) and give complete descriptions for each one of them. We provide some examples to show the relationships between them as well as with STi-space.

scholarly journals Some Applications of Supra Preopen Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
M. E. El-Shafei ◽  
A. H. Zakari ◽  
T. M. Al-shami
Keyword(s):  
Topological Spaces ◽  
Difference Property ◽  
Boundary Points ◽  
Separation Axioms ◽  
The Difference

The aim of this work is to define some concepts on supra topological spaces using supra preopen sets and investigate main properties. We started this paper by correcting some results obtained in previous study and presenting further properties of supra preopen sets. Then, we introduce a concept of supra prehomeomorphism maps and discuss its main properties. After that we explore the concepts of supra limit and supra boundary points of a set with respect to supra preopen sets and examine their behaviours on the spaces that possess the difference property. Finally, we formulate the concepts of supra pre-Ti-spaces i=0,1,2,3,4 and give completely descriptions for each one of them. In general, we study their main properties in detail and show the implications of these separation axioms among themselves as well as with STi-space with the help of some interesting examples.

scholarly journals £-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 53
Author(s):  
Fahad Alsharari
Keyword(s):  
Topological Spaces ◽  
Neutrosophic Sets ◽  
Extremally Disconnected ◽  
Fundamental Properties ◽  
Separation Axioms ◽  
New Concepts ◽  
Definition Of

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.

scholarly journals A Novel Hybrid Fuzzy Grey TOPSIS Method: Supplier Evaluation of a Collaborative Manufacturing Enterprise

2019 ◽  
Vol 9 (18) ◽  
pp. 3770 ◽  
Author(s):  
Yixiong Feng ◽  
Zhifeng Zhang ◽  
Guangdong Tian ◽  
Amir Mohammad Fathollahi-Fard ◽  
Nannan Hao ◽  
...  
Keyword(s):  
Decision Making ◽  
Comprehensive Evaluation ◽  
Real Life ◽  
Fuzzy Topsis ◽  
Supplier Evaluation ◽  
Manufacturing Enterprise ◽  
Collaborative Manufacturing ◽  
Life Problems ◽  
Order Preference ◽  
The Difference

Recently, there is of significant interest in developing multi-criteria decision making (MCDM) techniques with large applications for real-life problems. Making a reasonable and accurate decision on MCDM problems can help develop enterprises better. The existing MCDM methods, such as the grey comprehensive evaluation (GCE) method and the technique for order preference by similarity to an ideal solution (TOPSIS), have their one-sidedness and shortcomings. They neither consider the difference of shape and the distance of the evaluation sequence of alternatives simultaneously nor deal with the interaction that universally exists among criteria. Furthermore, some enterprises cannot consult the best professional expert, which leads to inappropriate decisions. These reasons motivate us to contribute a novel hybrid MCDM technique called the grey fuzzy TOPSIS (FGT). It applies fuzzy measures and fuzzy integral to express and integrate the interaction among criteria, respectively. Fuzzy numbers are employed to help the experts to make more reasonable and accurate evaluations. The GCE method and the TOPSIS are combined to improve their one-sidedness. A case study of supplier evaluation of a collaborative manufacturing enterprise verifies the effectiveness of the hybrid method. The evaluation result of different methods shows that the proposed approach overcomes the shortcomings of GCE and TOPSIS. The proposed hybrid decision-making model provides a more accurate and reliable method for evaluating the fuzzy system MCDM problems with interaction criteria.

scholarly journals A Comparative Study on Meta-Heuristic Algorithms For Solving the RNP Problem

2019 ◽  
pp. 1639-1648
Author(s):  
Abeer Sufyan Khalil ◽  
Rawaa Dawoud Al-Dabbagh
Keyword(s):  
Heuristic Algorithms ◽  
Real Life ◽  
Research Area ◽  
Optimization Techniques ◽  
Radio Network ◽  
Life Problems ◽  
Adaptive Differential Evolution ◽  
Low Efficiency ◽  
The Many

The continuous increases in the size of current telecommunication infrastructures have led to the many challenges that existing algorithms face in underlying optimization. The unrealistic assumptions and low efficiency of the traditional algorithms make them unable to solve large real-life problems at reasonable times.The use of approximate optimization techniques, such as adaptive metaheuristic algorithms, has become more prevalent in a diverse research area. In this paper, we proposed the use of a self-adaptive differential evolution (jDE) algorithm to solve the radio network planning (RNP) problem in the context of the upcoming generation 5G. The experimental results prove the jDE with best vector mutation surpassed the other metaheuristic variants, such as DE/rand/1 and classical GA, in term of deployment cost, coverage rate and quality of service (QoS).

WEAK TYPES OF LIMIT POINTS AND SEPARATION AXIOMS ON SUPRA TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (10) ◽  
pp. 8017-8036
Author(s):  
T. M. Al-shami ◽  
B. A. Asaad ◽  
M. K. El-bably
Keyword(s):  
Topological Spaces ◽  
Separation Axioms ◽  
Limit Points

scholarly journals Some Results on (Generalized) Fuzzy Multi-Hv-Ideals of Hv-Rings

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1376 ◽  
Author(s):  
Madeline Al Tahan ◽  
Sarka Hoskova-Mayerova ◽  
Bijan Davvaz
Keyword(s):  
Social Sciences ◽  
Real Life ◽  
Life Problems ◽  
New Concepts

The concept of fuzzy multiset is well established in dealing with many real life problems. It is possible to find various applications of algebraic hypercompositional structures in natural, technical and social sciences, where symmetry, or the lack of symmetry, is clearly specified and laid out. In this paper, we use fuzzy multisets to introduce the concept of fuzzy multi- H v -ideals as a generalization of fuzzy H v -ideals. Moreover, we introduce the concept of generalized fuzzy multi- H v -ideals as a generalization of generalized fuzzy H v -ideals. Finally, we investigate the properties of these new concepts and present different examples.

An Introduction to Deep Convolutional Neural Networks With Keras

2020 ◽  
pp. 231-272
Author(s):  
Wazir Muhammad ◽  
Irfan Ullah ◽  
Mohammad Ashfaq
Keyword(s):  
Graphics Processing Units ◽  
Real Life ◽  
Research Area ◽  
Training Data ◽  
Training Procedure ◽  
Deep Convolutional Neural Networks ◽  
Data Set ◽  
Life Problems ◽  
Graphics Processing ◽  
And Training

Deep learning (DL) is the new buzzword for researchers in the research area of computer vision that unlocked the doors to solving complex problems. With the assistance of Keras library, machine learning (ML)-based DL and various complicated or unresolved issues such as face recognition and voice recognition might be resolved easily. This chapter focuses on the basic concept of Keras-based framework DL library to handle the different real-life problems. The authors discuss the codes of previous libraries and same code run on Keras library and assess the performance on Google Colab Cloud Graphics Processing Units (GPUs). The goal of this chapter is to provide you with the newer concept, algorithm, and technology to solve the real-life problems with the help of Keras framework. Moreover, they discuss how to write the code of standard convolutional neural network (CNN) architectures using Keras libraries. Finally, the codes of validation and training data set to start the training procedure are explored.

(α,β)-Soft Intersectional Rings and Ideals with their Applications

2019 ◽  
Vol 15 (02) ◽  
pp. 333-350 ◽  
Author(s):  
Chiranjibe Jana ◽  
Madhumangal Pal ◽  
Faruk Karaaslan ◽  
Aslihan Sezgi̇n
Keyword(s):  
Set Theory ◽  
Real Life ◽  
Ring Structure ◽  
Ring Theory ◽  
Mathematical Framework ◽  
Soft Sets ◽  
Life Problems ◽  
New Concepts ◽  
Ring Structures ◽  
Algebraic Tool

Molodtsov initiated the soft set theory, providing a general mathematical framework for handling uncertainties that we encounter in various real-life problems. The main object of this paper is to lay a foundation for providing a new soft algebraic tool for considering many problems that contain uncertainties. In this paper, we introduce a new kind of soft ring structure called [Formula: see text]-soft-intersectional ring based on some results of soft sets and intersection operations on sets. We also define [Formula: see text]-soft-intersectional ideal and [Formula: see text]-soft-intersectional subring, and investigate some of their properties using these new concepts. We obtain some results in ring theory based on [Formula: see text]-soft intersection sense and its application in ring structures. Furthermore, we provide relationships between soft-intersectional ring and [Formula: see text]-soft-intersectional ring, soft-intersectional ideal and [Formula: see text]-soft-intersectional ideal.

Minimal structure approximation space and some of its application

2021 ◽  
Vol 40 (1) ◽  
pp. 973-982
Author(s):  
M. M. El-Sharkasy
Keyword(s):  
Information System ◽  
Binary Relation ◽  
Real Life ◽  
Approximation Space ◽  
Generalized System ◽  
Separation Axioms ◽  
Life Problems ◽  
Minimal Structure ◽  
Starting Point ◽  
New Space

Topological concepts play an important role in applications and solving real-life problems. Among of these concepts are neighbourhood and minimal structure. In this paper, we introduce a new space-based on a generalized system with a binary relation on a nonempty set by using the concept of a minimal structure, which is called a minimal structure approximation space (briefly, MSAS), and study some of its properties. Also, we compare the advantages of MSAS with neighbourhood approximation space which are based on the same starting point, and apply the concept of MSAS in some examples of chemistry to extraction and reduct the information. Finally, we investigate the concepts of the separation axioms on MSAS and study some of its properties in the information system as the process of approximation of information.

scholarly journals Two types of separation axioms on supra soft topological spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 147-165 ◽  
Author(s):  
Tareq M. Al-shami ◽  
Mohammed E. El-Shafei
Keyword(s):  
General Class ◽  
Topological Spaces ◽  
Finite Product ◽  
Soft Sets ◽  
Separation Axioms ◽  
Continuous Mappings ◽  
The Difference

AbstractIn 2011, Shabir and Naz [1] employed the notion of soft sets to introduce the concept of soft topologies; and in 2014, El-Sheikh and Abd El-Latif [2] relaxed the conditions of soft topologies to construct a wider and more general class, namely supra soft topologies. In this disquisition, we continue studying supra soft topologies by presenting two kinds of supra soft separation axioms, namely supra soft Ti-spaces and supra p-soft Ti-spaces for i = 0, 1, 2, 3, 4. These two types are formulated with respect to the ordinary points; and the difference between them is attributed to the applied non belong relations in their definitions.We investigate the relationships between them and their parametric supra topologies; and we provide many examples to separately elucidate the relationships among spaces of each type. Then we elaborate that supra p-soft Ti-spaces are finer than supra soft Ti-spaces in the case of i = 0, 1, 4; and we demonstrate that supra soft T3-spaces are finer than supra p-soft T3-spaces.We point out that supra p-soft Ti-axioms imply supra p-soft Ti−1, however, this characterization does not hold for supra soft Ti-axioms (see, Remark (3.30)). Also, we give a complete description of the concepts of supra p-soft Ti-spaces (i = 1, 2) and supra p-soft regular spaces. Moreover,we define the finite product of supra soft spaces and manifest that the finite product of supra soft Ti (supra p-soft Ti) is supra soft Ti (supra p-soft Ti) for i = 0, 1, 2, 3. After investigating some properties of these axioms in relation with some of the supra soft topological notions such as supra soft subspaces and enriched supra soft topologies, we explore the images of these axioms under soft S*-continuous mappings. Ultimately, we provide an illustrative diagram to show the interrelations between the initiated supra soft spaces.

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