Cargando…

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 neighbo...

Descripción completa

Detalles Bibliográficos
Autores principales: El Atik, Abd El Fattah, Nawar, Ashraf, Atef, Mohammed
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7643720/
http://dx.doi.org/10.1007/s41066-020-00245-z
_version_ 1783606334378213376
author El Atik, Abd El Fattah
Nawar, Ashraf
Atef, Mohammed
author_facet El Atik, Abd El Fattah
Nawar, Ashraf
Atef, Mohammed
author_sort El Atik, Abd El Fattah
collection PubMed
description 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.
format Online
Article
Text
id pubmed-7643720
institution National Center for Biotechnology Information
language English
publishDate 2020
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-76437202020-11-06 Rough approximation models via graphs based on neighborhood systems El Atik, Abd El Fattah Nawar, Ashraf Atef, Mohammed Granul. Comput. Original Paper 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. Springer International Publishing 2020-11-05 2021 /pmc/articles/PMC7643720/ http://dx.doi.org/10.1007/s41066-020-00245-z Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Original Paper
El Atik, Abd El Fattah
Nawar, Ashraf
Atef, Mohammed
Rough approximation models via graphs based on neighborhood systems
title Rough approximation models via graphs based on neighborhood systems
title_full Rough approximation models via graphs based on neighborhood systems
title_fullStr Rough approximation models via graphs based on neighborhood systems
title_full_unstemmed Rough approximation models via graphs based on neighborhood systems
title_short Rough approximation models via graphs based on neighborhood systems
title_sort rough approximation models via graphs based on neighborhood systems
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7643720/
http://dx.doi.org/10.1007/s41066-020-00245-z
work_keys_str_mv AT elatikabdelfattah roughapproximationmodelsviagraphsbasedonneighborhoodsystems
AT nawarashraf roughapproximationmodelsviagraphsbasedonneighborhoodsystems
AT atefmohammed roughapproximationmodelsviagraphsbasedonneighborhoodsystems