# Abdelfattah A. El-Atik

## Tanta University

H-index: 16

Africa-Egypt

## About Abdelfattah A. El-Atik

Abdelfattah A. El-Atik, With an exceptional h-index of 16 and a recent h-index of 13 (since 2020), a distinguished researcher at Tanta University, specializes in the field of Mathematics, Topology, Graph theory.

His recent articles reflect a diverse array of research interests and contributions to the field:

Some Topological Approaches of Rough Sets through Minimal Neighborhoods and Decision Making

Mathematical Morphology View of Topological Rough Sets and Its Applications

Topological representations of simplicial complexes and their applications

Generalized Rough Neighborhood Approximations and Related Topological Approaches

Covering Rough Sets in Terms of Topological Bi-Neighbourhoods and Their Applications

Fuzzy Soft Sets and Decision Making in Ideal Nutrition

Approximation of simplicial complexes using matroids and rough sets

Mutation of DNA and RNA sequences through the application of topological spaces

### Abdelfattah A. El-Atik Information

University | Tanta University |
---|---|

Position | Mathematics Department Faculty of Science Egypt |

Citations(all) | 799 |

Citations(since 2020) | 537 |

Cited By | 368 |

hIndex(all) | 16 |

hIndex(since 2020) | 13 |

i10Index(all) | 20 |

i10Index(since 2020) | 16 |

University Profile Page | Tanta University |

#### Abdelfattah A. El-Atik Skills & Research Interests

Mathematics

Topology

Graph theory

## Top articles of Abdelfattah A. El-Atik

### Some Topological Approaches of Rough Sets through Minimal Neighborhoods and Decision Making

Rough set has an important role to deal with uncertainty objects. The aim of this article is to introduce some kinds of generalization for rough sets through minimal neighborhoods using special kinds of binary relations. Moreover, four different types of dual approximation operators will be constructed in terms of minimal neighborhoods. The comparison between these types of approximation operators is discussed. Some new kinds of topological structures induced by minimal neighborhoods are established and some of their properties are studied. Finally, we give a comparison between these topologies that help for determining the major components of COVID-19 infections. In this application, the components of infections help the expert in decision making in medicine.

Authors

Ismail Shbair,Amgad Salama,Osama Embaby,Abdelfattah El-Atik

Journal

Journal of Mathematics

Published Date

2024/3/18

### Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets, mainly based on the context of image retrieval and the basic image correspondence problem. Mathematical morphological procedures and set approximations in rough set theory have some clear parallels. Numerous initiatives have been made to connect rough sets with mathematical morphology. Numerous significant publications have been written in this field. Others attempt to show a direct connection between mathematical morphology and rough sets through relations, a pair of dual operations, and neighborhood systems. Rough sets are used to suggest a strategy to approximate mathematical morphology within the general paradigm of soft computing. A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology. This paper …

Authors

Ibrahim Noaman,Abd El Fattah El Atik,Tamer Medhat

Journal

Computers, Materials & Continua

Published Date

2023/3/1

### Topological representations of simplicial complexes and their applications

Topological models can be used to represent complex systems which originate in the real life world. The aim of this paper is to show the equivalence between complexes and finite spaces. Complexes are used to build topological spaces from a set of vertices, edges and faces under constructing a finite number of building blocks. We study a transformation to illustrate the complex networks of the human brain to simplices. Finally, we give a topological model for simplicial complexes. In this case, we represent the brain as a union of simplicial complexes which may be used to give a diagnosis for a brain cancer.

Authors

A.A. El-Atik,A.A Azzam

Journal

Afrika Matematika

Published Date

2023/3/19

### Generalized Rough Neighborhood Approximations and Related Topological Approaches

This work aims to generate some types of M_ (j)–neighborhoods. Relationships among these M_ (j)-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_ (j)-lower, M_ (j)-upper approximations and M_ (j)-accuracy in terms of M_ (j)-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_ (j) approach and other approaches.

Authors

Amgad Salem Salama,Abdelfattah A El-Atik,Ali Hussein Salem,Osamy Embaby,Mona Samy Bondok

Published Date

2023/8/15

### Covering Rough Sets in Terms of Topological Bi-Neighbourhoods and Their Applications

Neighbourhoods are one of the important topics in topology that relies on two types of neighbours of a point and has many applications in the graph theory and in the sciences and medical sciences. In this work, some types of bi-j-neighbourhoods on generalized bicovering approximation space are introduced. Moreover, some kinds of bicovering rough sets using relations are presented. Some properties of these new types of covering are discussed. Pawlaks’ properties are studied in the case of bicovering approximation space. More properties on different bi-neighbourhoods such as bi-j-neighbourhoods, complementary bi-j-neighbourhoods, and bi-j-adhesions are investigated. A comparison between these new types of -neighbourhoods and -covering is presented with the help of some counterexamples. Finally, we give an application of our results in the rheumatic fever data information by generated topologies.

Authors

Amal T Abushaaban,Abdelfattah A El Atik,OA Embaby

Journal

Journal of Mathematics

Published Date

2023/2/28

### Fuzzy Soft Sets and Decision Making in Ideal Nutrition

Issues in daily life, where making the best decisions is crucial, are frequently encountered. But, in the majority of these situations, the best course of action is uncertain. We must take into account a number of parameters in order to find the best possible solution to these difficulties. The best mathematical instrument for this is fuzzy soft set FSS theory in decision making. Nutrition is the process of supplying cells and organisms with the nutrients they need to grow and thrive and to sustain life. A healthy diet has the potential to prevent or mitigate numerous prevalent health issues. The purpose of this paper is to select a burning problem for the nutrition of students and successfully apply the FSS theory in decision making. We aim to prove that the approach to decision-making problems with imprecise data via FSSs is more accurate than other types of approaches, and we present a new approach to the FSS model and its applications in decision-making problems.

Authors

Abdelfattah A El-Atik,Radwan Abu-Gdairi,Arafa A Nasef,Saeid Jafari,Mohammed Badr

Journal

Symmetry

Published Date

2023/8/2

### Approximation of simplicial complexes using matroids and rough sets

Matroid models are used to approximate complex systems that can be used to solve problems in the real world. The main goal of this paper is to show how matrices and rough sets on simplicial complexes can be used to create new types of matroids called simplicial matroids. We will look at some of their material properties. Because of these results, we are interested in learning about circuit and base axioms, rank functions, and closure operators. We also give more equivalent relations that can be used to make other equivalent simplicial matroids, such as 2-circuit simplicial matroids.

Authors

Abd El Fattah El Atik

Journal

Soft Computing

Published Date

2023/1/6

### Mutation of DNA and RNA sequences through the application of topological spaces

Topology is branch of modern mathematics that plays an important role in applications of biology. The aim of this paper is to study DNA sequence mutations using multisets, relations, metric functions, topology and association indices. Moreover, we use association indices to study the similarity between DNA sequences. These different ways of identifying a mutation help biologists to make a decision. A decision of mutation that depends on metrics between two sequences of genes and the topological structure produced by their relationship is presented.

Authors

A El-Atik,Y Tashkandy,S Jafari,AA Nasef,W Emam,M Badr

Journal

AIMS Math

Published Date

2023

### Research Article Covering Rough Sets in Terms of Topological Bi-Neighbourhoods and Their Applications

Neighbourhoods are one of the important topics in topology that relies on two types of neighbours of a point and has many applications in the graph theory and in the sciences and medical sciences. In this work, some types of bi• j• neighbourhoods on generalized bicovering approximation space are introduced. Moreover, some kinds of bicovering rough sets using relations are presented. Some properties of these new types of covering are discussed. Pawlaks’ properties are studied in the case of bicovering approximation space. More properties on different bi• neighbourhoods such as bi• j• neighbourhoods, complementary bi• j• neighbourhoods, and bi• j• adhesions are investigated. A comparison between these new types of bi• neighbourhoods and bi• covering is presented with the help of some counterexamples. Finally, we give an application of our results in the rheumatic fever data information by generated topologies.

Authors

Amal T Abushaaban,Abdelfattah A El Atik,OA Embaby

Published Date

2023

### Odd harmonious labeling of the converse skew product of graphs

In this paper, we utilize the ideas of odd harmonious labeling and the converse skew product to obtain more odd harmonious graphs. Also, we investigate its α-labeling. Finally, we define with proof a necessary condition for preserving odd graceful.

Authors

HM Hafez,R El-Shanawany,AA El Atik

Published Date

2023/6

### Nearly open sets in infra topology and related infra continuity

Infra topology has efficient tools of knowledge discovery. It has many applications in graph theory, fractals and game theory. One of the aims of this paper is to study some near infra open sets in infra topological spaces. Additionally, some results for near infra open and closed sets are studied. In fact, the union of an infra preclosed set and an infra α-closed set is an infra preclosed set. While, the intersection of an infra α-open set and an infra β-open set is infra β-open. Moreover, infra β-continuity is introduced and the relationships between some types of infra continuous functions is discussed. A comparison between near infra open sets and some other types of near open sets is investigated. Also, A comparison between near infra open sets and some other types of near open sets is obtained. Finally, we introduce two examples on infra topology to satisfy the relationships between infra β-continuity and some other types of infra continuity.

Authors

Abdelfattah A A El-Atik,Arafa A Nasef

Journal

Journal of Contemporary Technology and Applied Engineering

Published Date

2023/9/19

### A model of π-pre-topological structures and related to human heart

In this paper, the generalization of pre-topological spaces called bipretopological spaces (briefly, π-pre-topology) depending on two pre-topologies on an arbitrary universal set has been introduced. New kinds of separations axioms on π-pre-topological spaces are established and some of their properties are investigated. A comparison between four separation axioms on π-pre-topological spaces and pre-topological spaces with different sorts of counterexamples are presented. The topological property for some π-pre-separation axioms are satisfied and its relation with disubgraphs are discussed. A human heart will be studied through it is generated digraph. It is noted that all separation axioms for human heart are not all satisfied.

Authors

H Saber Osman,SA El-Sheikh,Abdelaziz E Radwan,El Atik,Abd El Fattah

Journal

Journal of Intelligent & Fuzzy Systems

Published Date

2023

### Closure operators in terms of chromosomal mutations

Topology provides an easy mathematical method to express some problems and helps to access a mathematical model to find solutions of these problems. The aim of this paper is to provide a mathematical model of chromosomal mutations in terms of mathematical and topo-logical methods. Moreover, we verify the validity of the mathematical model through topological operators by matching the properties of the resulting spaces with the biological properties of each of the chromo-somal mutations.

Authors

El Atik,Abd El Fattah,Mohammed S Badr

Journal

International Journal of Mathematics & Computer Science

Published Date

2022/7/1

### Topological rough sets vs Kuratowski operator and its applications

Some new types of closure operators that are generalization of a Kuratowski operator are defined throughout this paper. From these operators, we give new models of upper approximations, lower approximations and boundary regions that are basic notions in rough set theory. So, we investigate new concepts of rough sets, exact sets and some of their properties are studied. New forms of topological structures in terms of closure operators are established.

Authors

MM El-Sharkasy

Published Date

2022/7/13

### Some betweenness relation topologies induced by simplicial complexes

This article aims to create an approximation space from any simplicial complex by representing a finite simplicial complex as a union of its components. These components are arranged into levels beginning with the highest-dimensional simplices. The universal set of the approximation space is comprised of a collection of all vertices, edges, faces, and tetrahedrons, and so on. Moreover, new types of upper and lower approximations in terms of a betweenness relation will be defined. A betweenness relation means that an element lies between two elements: an upper bound and a lower bound. In this work, based on Zhang et al.'s concept, a betweenness relation on any simplicial complex, which produces a set of order relations, is established and some of its topologies are studied.

Authors

Abd El Fattah El Atik,Ashgan Wahba

Journal

Hacettepe Journal of Mathematics and Statistics

Published Date

2022

### A model of hepatitis C and blood pressure via nano topological spaces

Rough sets concept are important in real life applications. A nano topological space became a new type of modern topology in terms of rough sets. In this paper, we aim to analyze some real life problems using nano topology, especially, in medicine. We find that the key factors is necessary to decide whether a patient has Hepatitis C or not. Also, we conclude the key attribute has close connection to the disease of high blood pressure or hypertension.

Authors

AA Nasef,AA El Atik,GK Revathi

Journal

Thai Journal of Mathematics

Published Date

2022/6/29

### A Topological Approach of a Human Heart via Nano Pre-ideality

A technique to construct new neighborhoods for vertices of graphs will be defined. In this paper, the blood circulation of a human body can be classified by nano pre-\emph {I}-open sets which is properly placed between nano openness and nano preopenness regardless the nano topological ideal. Also, we show that the class of nano pre-\emph {I}-open sets is properly placed between the classes of nano\emph {I}-open and nano preopen sets. We give a decomposition of nano\emph {I}-continuity by proving that a function $ f:(X,\tau,\emph {I})\longrightarrow (Y,\sigma) $ is nano\emph {I}-continuous if and only if it is nano pre-\emph {I}-continuous and nano*-\emph {I}-continuous. Finally, we extend the graph of a blood circulation for a human body with respect to ideals.

Authors

Abd El Fattah A. El Atik

Journal

Thai Journal of Mathematics

Published Date

2022/10/7

### Comparison of twelve types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

In this paper, we generalize six kinds of rough set models based on j-neighborhood space (i.e., reflexive 1 j-neighborhood rough set, reflexive 2 j-neighborhood rough set, reflexive 3 j-neighborhood rough set, similarity 4 j-neighborhood rough set, similarity 5 j-neighborhood rough set, and similarity 6 j-neighborhood rough set) and investigate some of their basic properties. Further, we propose a new neighborhood space called j-adhesion neighborhood based on six types of rough set models (i.e., reflexive 7 j-adhesion neighborhood rough set, reflexive 8 j-adhesion neighborhood rough set, reflexive 9 j-adhesion neighborhood rough set, similarity 10 j-adhesion neighborhood rough set, similarity 11 j-adhesion neighborhood rough set, and similarity 12 j-neighborhood rough set) to reduce the boundary region and the accuracy. The fundamental properties of approximation operators based on j-adhesion …

Authors

Mohammed Atef,Ahmed Mostafa Khalil,Sheng-Gang Li,Abdelfatah Azzam,Heng Liu,Abd El Fattah El Atik

Journal

Soft Computing

Published Date

2022/1

### Topological Models of Rough Sets and Decision Making of COVID-19

The basic methodology of rough set theory depends on an equivalence relation induced from the generated partition by the classification of objects. However, the requirements of the equivalence relation restrict the field of applications of this philosophy. To begin, we describe two kinds of closure operators that are based on right and left adhesion neighbourhoods by any binary relation. Furthermore, we illustrate that the suggested techniques are an extension of previous methods that are already available in the literature. As a result of these topological techniques, we propose extended rough sets as an extension of Pawlak’s models. We offer a novel topological strategy for making a topological reduction of an information system for COVID-19 based on these techniques. We provide this medical application to highlight the importance of the offered methodologies in the decision-making process to discover the important component for coronavirus (COVID-19) infection. Furthermore, the findings obtained are congruent with those of the World Health Organization. Finally, we create an algorithm to implement the recommended ways in decision-making.

Authors

Mostafa A El-Gayar,El Atik,Abd El Fattah

Journal

Complexity

Published Date

2022/6/24

### Topological kernel of sets and application on fractals

In various mathematical sciences, sets and functions in topology have been extensively developed and exploited. Some novel separation axioms have been discovered through studying generalizations of closures duo to closed sets, -sets, and -sets. Self similar fractals have important role in some real life problems as physics and engineering. In this paper, the topology described by the family of - and - sets in topological spaces is defined and studied in terms of -Sets and -Sets. Also, the topological space $\mathbf{Top_{(\X,\tau^{\bigwedge_{\delta\gamma}})}}$ is defined and studied. Additionally, several features of these sets are presented, as well as some associated new separation axioms. Finally, we improved theorems 4.3 \cite{CaldasJavNoi2000} and 6.5 \cite{Caldas2005} for Caldas et al. We approximate self similar fractals through graph theory to topological spaces. Some topological properties such as separation axioms are studied. Finally, the kernel of topological approximations of fractals are calculated in terms of their connecting points.

Authors

Abd El Fattah A El Atik,Arafa A Nasef

Journal

Journal of Contemporary Technology and Applied Engineering

Published Date

2022/10/2

### Topological visualization of rough sets by neighborhoods and a heart application based graphs

A human heart is represented by graph theory and has many topological formulations. The main purpose of the article is to introduce a special class of neighborhood systems, called 1-neighborhood systems (NSs for short), as tools to generalize rough set theory and give the human heart new modeling by using topological structures. Some new types of minimal neighborhoods and core minimal are introduced. A comparison between these new types of neighborhoods are discussed. In addition, new forms of topological spaces through a 1-NS of vertices for a graph of the human heart are presented and studied as a practical example in real-life problems. A best model of the topological structure which may be used for diagnosis is suggested.

Authors

Abd El-Fattah A El-Atik,Mostafa K El-Bably,Mostafa A El-Gayar

Published Date

2022/6/8

### More characterizations on ????????-compact spaces using grills

In this paper, we introduce a new class of compactness with grill such as G-???? ????-compact, G-strongly compact, G-???? compact and G-???? ????-compact spaces. Some of their properties and characterizations are obtained. Also, we define and study the concept of G-???? ????-compactness spaces under continuous functions.

Authors

RA Rashwan,El Atik,Abd El Fattah,Atef Hussien

Journal

J. Math. Comput. Sci.

Published Date

2022/8/22

### A topological representation of matroids using graphs

Matroids arise in combinatorial optimization since the greedymethod runs for structures. In this article, we study some fundamental matroid characteristics. Also, we build topologies generated by matroids with an equivalence relation. and we study the connectedness on matroids through their topological structures. Furthermore, we investigate simple graphs and matroid connectivity.

Authors

El Atik,Abd El Fattah,Sally Haroun

Journal

International Journal of Mathematics & Computer Science

Published Date

2022/7/1

### On irresolute multifunctions and related topological games

In this paper, we introduce and study α-irresolute multifunctions, and some of their properties are studied. The properties of α-compactness and α-normality under upper α-irresolute multifunctions are topological properties. Also, we prove that the composition of two upper and lower α-irresolute multifunctions is α-irresolute. We apply the results of α-irresolute multifunctions to topological games. Upper and lower topological games are introduced. The set of places for player ONE in upper topological games may guarantee a gain is semi-closed. Finally, some optimal strategies for topological games are defined and studied.

Authors

Sewalem Ghanem and Abdelfattah A. El Atik

Journal

AIMS Mathematics

Published Date

2022/8/22

### On grill nano topological spaces and its related with nano continuity

Some new concepts of grill nano topological structures throughout this paper are presented and studied. We generalize the famous closure operators that can be induced by binary operations. Some basic investigations for proposed structures are discussed. In addition, the connection between rough sets and grill set theory can be illustrated via some numerous examples. Finally, a comparison between proposed approaches and other studies is established.

Authors

M Lellis Thivagar,Atef Hussien

Journal

Journal of Physics: Conference Series

Published Date

2021/5/1

### Correct proof of the main result in “The number of spanning trees of a class of self-similar fractal models” by Ma and Yao

The problem of counting the number of spanning trees of a network built by a replacement procedure that yields a self-similar structure is considered. This problem has been receiving growing attention in the specialized literature in the recent years. One of the important measures of the global reliability of a network is the number of spanning trees. In this paper, we present a correction of the two main theorems claimed by Ma and Yao [7] concerning the number and the entropy of spanning trees of a class of self-similar fractal models with proofs of the new results. Also, the numerical values of the number of spanning trees are obtained and compared with the values of the formula in Theorem 3.1 of [7].

Authors

A.Elsaid Abd ElFattah A.ElAtik,A.W.Aboutahoun

Journal

Information Processing Letters

Published Date

2021

### More results on rough sets via neighborhoods of graphs with finite path

Rough set theory had been proposed by Pawlak in the early of 1982. The theory is a new mathematical tool to deal with vagueness and imperfect knowledge. In this paper, we study neighborhoods for vertices of graphs with length that at most 2 edges. A new binary relation induced from a simple graph is defined and more properties of star definability which based on reflexive and transitive relation will be discussed. So, we investigate N-star lower and N-star upper approximations, for every subset B of a set of vertices V of a graph G. The relationship between the star set and independent set will be discussed.

Authors

Abdel Monam Kozae,Sally Haroun

Journal

Journal of Physics: Conference Series

Published Date

2021/5/1

### Modelling pollution of radiation via topological minimal structures

The model of a generalized variable precision rough set is one of the variable precision rough sets used to solve some problems and measurements confront us that was difficult from the view point of science. The behavior of the radio contaminants in the environment is one of these measurements. Throughout this paper, we introduce and study a generalization variable precision rough set via a topological minimal structure. Some characteristics related to generalized upper and lower approximation with a variable precision by minimal structures will be discussed. A dispersion model which is the necessity to predict atmospheric path and danger from an atmospheric plume of hazardous materials will be applied with different types of examples.

Authors

A Abd El Fattah,Ibrahim Kamel Halfa,ABDELFATTAH AZZAM

Journal

Transactions of A. Razmadze Mathematical Institute

Published Date

2021/4

### Rough approximation models via graphs based on neighborhood systems

Neighborhood systems are used to approximate graphs as finite topological structures. Throughout this article, we construct new types of eight neighborhoods for vertices of an arbitrary graph, say, j-adhesion neighborhoods. Both notions of Allam et al. and Yao will be extended via j-adhesion neighborhoods. We investigate new types of j-lower approximations and j-upper approximations for any subgraph of a given graph. Then, the accuracy of these approximations will be calculated. Moreover, a comparison between accuracy measures and boundary regions for different kinds of approximations will be discussed. To generate j-adhesion neighborhoods and rough sets on graphs, some algorithms will be introduced. Finally, a sample of a chemical example for Walczak will be introduced to illustrate our proposed methods.

Authors

Abd El Fattah El Atik,Ashraf Nawar,Mohammed Atef

Journal

Granular computing

Published Date

2021/10

### Some extensions of covering-basedmultigranulation fuzzy rough sets from new perspectives

Covering-based multigranulation fuzzy rough sets are a natural extension of the multigranulation rough sets by replacing crisp sets with fuzzy sets. Recently, the covering-based multigranulation fuzzy rough sets in terms of the family of a fuzzy -neighborhoods is due to Zhan et al. (Artif Intell Rev 53(2):1093–1126). As a generalization to Zhan’s method which pointed to increase the lower approximation and decrease the upper approximation, the proposed article aims to introduce the notion of a family of fuzzy complementary -neighborhood and thus four types of covering-based optimistic (pessimistic) multigranulation fuzzy rough sets models are presented. Also, four new kinds of covering-based -optimistic (pessimistic) multigranulation fuzzy rough sets models are constructed. Some characterizations of these models and its related with Zhan’s model are studied. A comparison between these new …

Authors

Mohamed Atef and Abd El Fattah El Atik

Journal

Soft Computing

Published Date

2021/2/26

### Fuzzy topological structures via fuzzy graphs and their applications

Fuzzy graphs are an individual of application tools in the area of mathematics, which permit the users to define the relative between concepts because the wildlife of fuzziness is satisfactory for any situation. They are helpful to give more exactness and suppleness to the classification as associated with the traditional models. A topological structure is a set model for graphs. The main purpose of this paper is to introduce a new kind of fuzzy topological structures in terms of fuzzy graphs called fuzzy topological graphs due to a class of fuzzy subsets, and some of their properties are investigated. Also, a new procedure to calculate the number of edges in fuzzy graphs will be defined. Further, we consider the concept of a homeomorphic between fuzzy topological graphs as a fuzzy topological property that can be used to prove the isomorphic between fuzzy graphs. Moreover, an algorithm based on the proposed …

Authors

Abd El Fattah El Atik and Ashraf Nawar Mohamed Atef

Journal

Soft Computing

Published Date

2021/9/2

### Soft -rough sets and their application to determine COVID-19

Soft rough set theory has been presented as a basic mathematical model for decision-making for many real-life data. However, soft rough sets are based on a possible fusion of rough sets and soft sets which were proposed by Feng et al.[20]. The main contribution of the present article is to introduce a modification and a generalization for Feng's approximations, namely, soft -rough approximations, and some of their properties will be studied. A comparison between the suggested approximations and the previous one [20] will be discussed. Some examples are prepared to display the validness of these proposals. Finally, we put an actual example of the infections of coronavirus (COVID-19) based on soft -rough sets. This application aims to know the persons most likely to be infected with COVID-19 via soft -rough approximations and soft -rough topologies.

Authors

MOSTAFA K BABLY,ABD EL FATTAH A ATIK

Journal

Turkish Journal of Mathematics

Published Date

2021

### Topological approaches of graphs and their applications by neighborhood systems and rough sets

Rough set theory is used in simple directed graphs to study nano topology. Adjacent vertices was used in digraphs only to define their neighborhoods. Four types of neighborhood systems for vertices are introduced in this article which depend on both adjacent vertices and associated edges. Additionally, the generalization of some notions presented by Pawlak and Lellis Thivagar and some of their properties are investigated. Finally, we present a new model of a blood circulation system of the human heart based on blood paths. Also, different kinds of topological separation axioms are presented and studied between vertices and edges of the heart blood circulation model.

Authors

Abd El Fattah A El Atik

Journal

Journal of Intelligent & Fuzzy Systems

Published Date

2020/1/1

### Certain types of coverings based rough sets with application

Covering-based rough sets are important generalizations of the classical rough sets of Pawlak. In this paper, by means of j-neighborhoods, complementary j-neighborhoods and j-adhesions, we build some new different types of j-covering approximations based rough sets and study related properties. Also, we explore the relationships between the considered j-covering approximations and investigate the properties of them. Using different neighborhoods, some different general topologies are generated as topologies induced from a binary relation. Finally, an interesting application of the new types of covering-based rough sets to the rheumatic fever is given.

Authors

AS Nawar,MK El-Bably,Abd El Fattah El-Atik

Journal

Journal of Intelligent & Fuzzy Systems

Published Date

2020/8/28

### Reduction based on similarity and decision-making

Reduction of attributes in an information system (IS) is a basic step for IS analysis. The original rough set model of Pawlak depends on an equivalence relation which is strongly constraints. This paper aims to use similarity classes and similarity degrees to obtain a reduction of IS and indicate an approach by using an example from biochemistry to get a quantitative structure activity relationship (QSAR). Moreover, signs of each attribute and degrees of memberships are computed to give a decision by using the degree of similarity. The suggested approach gives an increase in decision-making and decision accuracy.

Authors

Abd El Fattah A El Atik

Journal

Journal of the Egyptian Mathematical Society

Published Date

2020/12

### Neutrosophic αψ-connectedness

Neutrosophic topological space is an extension of intuitionistic topological space and each triplet set in neutrosophic topological space contains membership, indeterminacy and non-membership values. Connected set in intuitionistic topological set contains membership and non-membership values and inderterminacy have not discussed in that set. This motivates the authors to propose this novel concept called neutrosophic αψ-connectedness. So we introduce the new notion of neutrosophic αψ-connectedness in neutrosophic topological spaces and investigate some properties of neutrosophic αψ-connectedness between sets and subsets of two sets. Some properties of this concept presented with numerical quantities to prove the non-existence.

Authors

M Parimala,M Karthika,Saeid Jafari,Florentin Smarandache,AA El-Atik

Journal

Journal of Intelligent & Fuzzy Systems

Published Date

2020/1/1

### Some nano topological structures via ideals and graphs

In this paper, new forms of nano continuous functions in terms of the notion of nano Iα-open sets called nano Iα-continuous functions, strongly nano Iα-continuous functions and nano Iα-irresolute functions will be introduced and studied. We establish new types of nano Iα-open functions, nano Iα-closed functions and nano Iα-homeomorphisms. A comparison between these types of functions and other forms of continuity will be discussed. We prove the isomorphism between simple graphs via the nano continuity between them. Finally, we apply these topological results on some models for medicine and physics which will be used to give a solution for some real-life problems.

Authors

Abd El-Fattah A El-Atik,Hanan Z Hassan

Journal

Journal of the Egyptian Mathematical Society

Published Date

2020/8/18

### Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

In this paper, we generalize three types of rough set models based on j-neighborhood space (ie, type 1 j-neighborhood rough set, type 2 j-neighborhood rough set, and type 3 j-neighborhood rough set), and investigate some of their basic properties. Also, we present another three types of rough set models based on j-adhesion neighborhood space (ie, type 4 j-adhesion neighborhood rough set, type 5 j-adhesion neighborhood rough set, and type 6 j-adhesion neighborhood rough set). The fundamental properties of approximation operators based on j-adhesion neighborhood space are established. The relationship between the properties of these types is explained. Finally, according to j-adhesion neighborhood space, we give a comparison between the Yao’s approach and our approach.

Authors

Mohammed Atef,Ahmed Mostafa Khalil,Sheng-Gang Li,AA Azzam,El Atik,Abd El Fattah

Journal

Journal of Intelligent & Fuzzy Systems

Published Date

2020/1/1

### Some topological structures of fractals and their related graphs

The aim of this paper is to introduce a topological model of fractals. Self similar fractals will be approached as inverse limit of finite one dimensional topological spaces with alpha continuous bonding functions. The second approach is to investigate topological graphs in terms nano topological spaces for Lellis Thivagar. From these approximations, the dynamics of Julia sets as a special type of self similar fractals will be studied and some physical properties of fractals through their nano topological graphs will be applied.

Authors

Atik Abd El Fattah A El,Arafa A Nasef

Journal

Filomat

Published Date

2020

## Abdelfattah A. El-Atik FAQs

### What is Abdelfattah A. El-Atik's h-index at Tanta University?

The h-index of Abdelfattah A. El-Atik has been 13 since 2020 and 16 in total.

### What are Abdelfattah A. El-Atik's top articles?

The articles with the titles of

Some Topological Approaches of Rough Sets through Minimal Neighborhoods and Decision Making

Mathematical Morphology View of Topological Rough Sets and Its Applications

Topological representations of simplicial complexes and their applications

Generalized Rough Neighborhood Approximations and Related Topological Approaches

Covering Rough Sets in Terms of Topological Bi-Neighbourhoods and Their Applications

Fuzzy Soft Sets and Decision Making in Ideal Nutrition

Approximation of simplicial complexes using matroids and rough sets

Mutation of DNA and RNA sequences through the application of topological spaces

...

are the top articles of Abdelfattah A. El-Atik at Tanta University.

### What are Abdelfattah A. El-Atik's research interests?

The research interests of Abdelfattah A. El-Atik are: Mathematics, Topology, Graph theory

### What is Abdelfattah A. El-Atik's total number of citations?

Abdelfattah A. El-Atik has 799 citations in total.

### What are the co-authors of Abdelfattah A. El-Atik?

The co-authors of Abdelfattah A. El-Atik are A.A.Nasef, Abdelmonem Mohamed Kozae, Shokry Nada, Ashraf Nawar, M. M. El-Sharkasy.