Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System

Magdy Salah El-Azab; Mohamed Shokry; Reham Emad Aly

doi:doi:10.11648/j.pamj.20211005.12

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Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System

Magdy Salah El-Azab, Mohamed Shokry, Reham Emad Aly

Published in Pure and Applied Mathematics Journal (Volume 10, Issue 5)

Received: 13 September 2021 Accepted: 11 October 2021 Published: 10 November 2021

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Abstract

The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.

Published in	Pure and Applied Mathematics Journal (Volume 10, Issue 5)
DOI	10.11648/j.pamj.20211005.12
Page(s)	107-120
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Graph Theory, Soft Set, Soft Graph Set, Rough Set Theory, The Cardiovascular System

References

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APA Style

Magdy Salah El-Azab, Mohamed Shokry, Reham Emad Aly. (2021). Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System. Pure and Applied Mathematics Journal, 10(5), 107-120. https://doi.org/10.11648/j.pamj.20211005.12

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ACS Style

Magdy Salah El-Azab; Mohamed Shokry; Reham Emad Aly. Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System. Pure Appl. Math. J. 2021, 10(5), 107-120. doi: 10.11648/j.pamj.20211005.12

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AMA Style

Magdy Salah El-Azab, Mohamed Shokry, Reham Emad Aly. Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System. Pure Appl Math J. 2021;10(5):107-120. doi: 10.11648/j.pamj.20211005.12

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@article{10.11648/j.pamj.20211005.12,
  author = {Magdy Salah El-Azab and Mohamed Shokry and Reham Emad Aly},
  title = {Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {5},
  pages = {107-120},
  doi = {10.11648/j.pamj.20211005.12},
  url = {https://doi.org/10.11648/j.pamj.20211005.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211005.12},
  abstract = {The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.},
 year = {2021}
}

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TY  - JOUR
T1  - Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System
AU  - Magdy Salah El-Azab
AU  - Mohamed Shokry
AU  - Reham Emad Aly
Y1  - 2021/11/10
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211005.12
DO  - 10.11648/j.pamj.20211005.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 107
EP  - 120
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211005.12
AB  - The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.
VL  - 10
IS  - 5
ER  -

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Author Information

Magdy Salah El-Azab

Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt
Mohamed Shokry

Physics and Engineering Mathematics Department, Faculty of Engineering, Tanta University, Seperbay, Tanta, Egypt
Reham Emad Aly

Physics and Engineering Mathematics Department, Higher Institute of Engineering and Technology in Damietta, New Damietta, Egypt

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Plain Text BibTeX RIS

APA Style

Magdy Salah El-Azab, Mohamed Shokry, Reham Emad Aly. (2021). Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System. Pure and Applied Mathematics Journal, 10(5), 107-120. https://doi.org/10.11648/j.pamj.20211005.12

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ACS Style

Magdy Salah El-Azab; Mohamed Shokry; Reham Emad Aly. Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System. Pure Appl. Math. J. 2021, 10(5), 107-120. doi: 10.11648/j.pamj.20211005.12

Copy | Download

AMA Style

Magdy Salah El-Azab, Mohamed Shokry, Reham Emad Aly. Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System. Pure Appl Math J. 2021;10(5):107-120. doi: 10.11648/j.pamj.20211005.12

Copy | Download

@article{10.11648/j.pamj.20211005.12,
  author = {Magdy Salah El-Azab and Mohamed Shokry and Reham Emad Aly},
  title = {Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {5},
  pages = {107-120},
  doi = {10.11648/j.pamj.20211005.12},
  url = {https://doi.org/10.11648/j.pamj.20211005.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211005.12},
  abstract = {The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System
AU  - Magdy Salah El-Azab
AU  - Mohamed Shokry
AU  - Reham Emad Aly
Y1  - 2021/11/10
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211005.12
DO  - 10.11648/j.pamj.20211005.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 107
EP  - 120
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211005.12
AB  - The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.
VL  - 10
IS  - 5
ER  -

Copy | Download