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Some new approaches to neighborhoods via graphs

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

This paper aims to increase the accuracy measure of the subgraph of a graph and generate new nano topologies on the power set of vertices and edges of a graph. Firstly, we introduce \({\mathcal {E}}_j\)-neighborhoods and \({\mathcal {C}}_j\)-neighborhoods which depend on vertices and edges of a simple directed graph by using j-neighborhoods for \(j\in \{\text {out}, \text {in}, \cap , \cup \}\). Then, we apply these neighborhoods to present the concepts of \({\mathcal {E}}_j\)-approximations and \({\mathcal {C}}_j\)-approximations. We investigate their main properties and relationships among them. Besides, we define the accuracy measures of a subgraph with the help of these approximations and show that \({\mathcal {C}}_j\)-accuracy measures are the highest when we compare these accuracy measures with the previous one. Furthermore, we generate new nano topologies via obtained approximations and illustrate that these topologies may not be comparable. Finally, we give an application in physics to elucidate the current approximations are more general. Throughout the paper, we summarize all comparisons with tables and give counterexamples to support the study.

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References

  • Abd El-Monsef ME, Embaby OA, El-Bably MK (2014) Comparison between rough set approximations based on different topologies. Int. J Granular Computing, Rough Sets and Intelligent Systems, 3(4), 292- 305

  • Al-shami TM (2021) An improvement of rough sets accuracy measure using containment neighborhoods with a medical application. Inf Sci 569:110–124

  • Al-shami TM, Fu WQ, Abo-Tabl EA (2021) New rough approximations based on \(E_j\)-neighborhoods. Complexity, 2021: 6666853, 6 pages

  • Al-shami TM, Ciucci D (2022) Subset neighborhood rough sets. Knowl-Based Syst 237:107868

    Article  Google Scholar 

  • Atef M, Khalil AM, Li S, Azzam A, El-Atik AEF (2020) Comparison of six types of rough approximations based on j -neighborhood space and j -adhesion neighborhood space. J Intel Fuzzy Syst 39(3):4515–4531

    Article  Google Scholar 

  • Bondy JA, Murty USR (1976) Graph theory with applications. Elsevier Science Publishing Co., Inc.,

  • Bondy JA, Murty USR (2008) Graph Theory. Springer, Berlin

    Book  MATH  Google Scholar 

  • Boruah C, Gogoi K, Chutia C (2017) Analysis of some electrical circuits with the help of graph theory using network equilibrium equations. I. J Innovat Res Sci, Eng Technol, 6(1): 944-953

  • Chen J, Li J (2012) An application of rough sets to graph theory. Inf Sci 201:114–127

    Article  MATH  Google Scholar 

  • El Atik A, Hassan H (2020) Some nano topological structures via ideals and graphs. J Egypt Math Soc 28(41):1–21

    MATH  Google Scholar 

  • El Atik A, Nasef A (2020) Some topological structures of fractals and their related graphs. Filomat 34(1):153–165

    Article  MATH  Google Scholar 

  • El Atik AA, Wahba AS (2020) Topological approaches of graphs and their applications by neigborhood systems and rough sets. J Intell Fuzzy Syst. 39(5): 6979-6992

  • Järvinen J (2007) Lattice theory for rough sets, Transactions on Rough Sets VI. LNSC, Springer-Verlag, Berlin, Heidelberg 24374(6):400–498

    MATH  Google Scholar 

  • Nada SI, El-Atik AA, Atef M (2018) New types of topological structures via graphs. Math Methods Appl Sci 41(15):5801–5810

    Article  MATH  Google Scholar 

  • Nasef A, El Atik AA (2017) Some properties on nano topology induced by graphs. AASCIT J Nanosci 3(4):19–23

    Google Scholar 

  • Nawar AS, El Atik AA (2019) A model of a human heart via graph nano topological spaces. Int J Biomath 12(1). https://doi.org/10.1142/S1793524519500062

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

  • Pawlak Z (1991) Kluwer Academic Publishers, Dordrecht, The Netherlands, Rough Sets-Theoretical Aspects of Reasoning about Data

  • Thivagar ML, Richard C (2013) On nano forms of weakly open sets. Int J Math Stat Inven 1:31–37

    Google Scholar 

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Acknowledgements

The authors would like to thank the referees and the editor for their helpful suggestions.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Ege University, 35100, İzmir, Turkey

    A. Ç. Güler & O. B. Özbakir

  2. Faculty of Science and Letters, Department of Mathematics, Yaşar University, 35100, İzmir, Turkey

    E. D. Yildirim

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  1. A. Ç. Güler
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  2. E. D. Yildirim
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  3. O. B. Özbakir
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The authors contributed equally to this work. The authors read and approved the final manuscript.

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Correspondence to A. Ç. Güler.

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Güler, A.Ç., Yildirim, E.D. & Özbakir, O.B. Some new approaches to neighborhoods via graphs. Soft Comput 27, 1303–1315 (2023). https://doi.org/10.1007/s00500-022-07732-2

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