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A new approximation technique based on central bodies of rough fuzzy directed graphs for agricultural development

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Abstract

The identification of central body in directed networks is critical as it shows the areas of the network that require attention by cutting through noisy data. In network theory, the measures of centrality offer numbers or values to nodes within a graph related to their network location. Many centrality measures already exist in different network models. However, these centrality measures are generally based on membership values of edges, and there is no widely acknowledged method to assess the efficacy and reliability of these measures when dealing with incomplete and ambiguous information concurrently. Therefore, we suggest an innovative perspective where centrality measures are introduced in rough fuzzy directed (RFD) network model that is a predominant approach for dealing incomplete and ambiguous information simultaneously. Based on the connectedness of the RFD network, the in-degree centrality \(C_{id}\), out-degree centrality \(C_{od}\), in-closeness centrality \(C_{ic}\) and out-closeness centrality \(C_{oc}\) are defined and characterized for its bounds. Expressions for centrality measures of rough fuzzy directed path networks and rough fuzzy directed cycle networks are generalized. Finally, this conceptual structure is applied to the decision-making of effective management of water supply system and it is used to assess and compare different approaches. The traditional centrality measures are found to perform poorly on a large number of networks, indicating inherent limits for expressing the centrality of nodes in complicated networks.

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References

  1. Ahmad, U., Batool, T.: Domination in rough fuzzy digraphs with application. Soft. Comput. 27, 2425–2442 (2023)

    Article  Google Scholar 

  2. Ahmad, U., Nawaz, I.: Directed rough fuzzy graph with application to trade networking. Comput. Appl. Math. 41, 366 (2022)

    Article  MathSciNet  Google Scholar 

  3. Ahmad, U., Nawaz, I.: Wiener index of a directed rough fuzzy graph and application to human trafficking. J. Intell. Fuzzy Syst. 44, 1479–1495 (2023)

    Article  Google Scholar 

  4. Ahmad, U., Sabir, M.: Multicriteria decision making based on the degree and distance based indices of fuzzy graphs. Gran. Comput. 8, 793–807 (2023)

    Article  Google Scholar 

  5. Ahmad, U., Khan, N.K., Saeid, A.B.: Fuzzy topological indices with application to cybercrime problem. Gran. Comput. 8, 967–980 (2023)

    Article  Google Scholar 

  6. Ahmad, U., Nawaz, I., Broumi, S.: Connectivity index of directed rough fuzzy graphs and its application in traffic flow network. Gran. Comput. 8, 1561–1582 (2023)

    Article  Google Scholar 

  7. Akram, M., Arshad, M.: Fuzzy rough graph theory with applications. Int. J. Comput. Intell. Syst. 12, 90–107 (2018)

    Article  Google Scholar 

  8. Akram, M., Arshad, M.: A new approach based on fuzzy rough digraphs for decision-making. J. Intell. Fuzzy Syst. 35, 2105–2121 (2018)

    Article  Google Scholar 

  9. Akram, M., Siddique, S., Alcantud, J.C.R.: Connectivity indices of m-polar fuzzy network model with an application to a product manufacturing problem. Artif. Intell. Rev. 56, 7795–7838 (2023)

    Article  Google Scholar 

  10. Akram, M., Zafar, F.: Multi-criteria decision-making methods under soft rough fuzzy knowledge. J. Intell. Fuzzy Syst. 35, 3507–3528 (2018)

    Article  Google Scholar 

  11. Akram, M., Zafar, F.: Rough fuzzy digraphs with application. J. Appl. Math. Comput. 59(1), 91–127 (2019)

    Article  MathSciNet  Google Scholar 

  12. Akram, M., Zafar, F.: A new approach to compute measures of connectivity in rough fuzzy network models. J. Intell. Fuzzy Syst. 36(1), 449–465 (2019)

    Article  Google Scholar 

  13. Akram, M., Zafar, F.: Hybrid Soft Computing Models Applied to Graph Theory. Springer International Publishing (2020). https://doi.org/10.1007/978-3-030-16020-3

  14. Borzooei, R.A., Rashmanlou, H.: Domination in vague graphs and its applications. J. Intell. Fuzzy Syst. 29(5), 1933–1940 (2015)

    Article  MathSciNet  Google Scholar 

  15. Borzooei, R.A., Rashmanlou, H.: Degree of vertices in vague graphs. J. Appl. Math. Inf. 33(5), 545–557 (2015)

    MathSciNet  Google Scholar 

  16. Dhanalakshmi, R., Rashid, J., Kim, J., Sivaraman, A.K., Naseem, U., Vincent, R.: A new method for centrality measurement using generalized fuzzy graphs. Discr. Dyn. Nat. Soc. (2022). https://doi.org/10.1155/2022/4704409

    Article  Google Scholar 

  17. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gener. Syst. 17(2–3), 191–209 (1990)

    Article  Google Scholar 

  18. Freeman, L.C.: Centrality in social networks: conceptual clarification social network. Crit. Concepts Sociol. 1, 238–263 (2002)

    Google Scholar 

  19. Habib, A., Akram, M., Kahraman, C.: Minimum spanning tree hierarchical clustering algorithm: a new Pythagorean fuzzy similarity measure for the analysis of functional brain networks. Expert Syst. Appl. 201, 117016 (2002)

    Article  Google Scholar 

  20. Huang, A., Zhu, W.: Connectedness of graphs and its application to connected matroids through covering-based rough sets. Soft. Comput. 20(5), 1841–1851 (2016)

    Article  Google Scholar 

  21. Hu, R.J., Li, Q., Zhang, G.Y., Ma, W.C.: Centrality measures in directed fuzzy social networks. Fuzzy Inf. Eng. 7(1), 115–128 (2015)

    Article  MathSciNet  Google Scholar 

  22. Katz, L.X.: A new status index derived from sociometric analysis. Psychometrika 18(1), 39–43 (1953)

    Article  Google Scholar 

  23. Mordeson, J.N., Chang-Shyh, P.: Operations on fuzzy graphs. Inf. Sci. 79(3–4), 159–170 (1994)

    Article  MathSciNet  Google Scholar 

  24. Nieminen, J.: On the centrality in a graph. Scand. J. Psychol. 15(1), 332–336 (1974)

    Article  MathSciNet  Google Scholar 

  25. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982)

    Article  Google Scholar 

  26. Rashmanlou, H., Samanta, S., Pal, M., Borzooei, R.A.: Bipolar fuzzy graphs with categorical properties. Int. J. Comput. Intell. Syst. 8(5), 808–818 (2015)

    Article  Google Scholar 

  27. Rosenfeld, A.: Fuzzy graphs. In: Fuzzy Sets and Their Applications to Cognitive and Decision Processes. Academic Press, pp. 77–95 (1975)

  28. Sabidussi, G.: The centrality index of a graph. Psychometrika 31(4), 581–603 (1996). https://doi.org/10.1007/BF02289527

    Article  MathSciNet  Google Scholar 

  29. Shimbel, A.: Structural parameters of communication networks. Bull. Math. Biophys. 15, 501–507 (1953)

    Article  MathSciNet  Google Scholar 

  30. Talebi, A.A., Rashmanlou, H., Sadati, S.H.: Interval-valued intuitionistic fuzzy competition graph. J. Multiple-Valued Logic Soft Comput. 34(3–4), 335–364 (2020)

    MathSciNet  Google Scholar 

  31. Zeng, S., Shoaib, M., Ali, S., Smarandache, F., Rashmanlou, H., Mofidnakhaei, F.: Certain properties of single-valued neutrosophic graph with application in food and agriculture organization. Int. J. Comput. Intell. Syst. 14(1), 1516–1540 (2021)

    Article  Google Scholar 

  32. Wang, D., Zhu, P.: Graph reduction in a path information-based rough directed graph model. Soft. Comput. 26(9), 4171–4186 (2022)

    Article  Google Scholar 

  33. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  34. Zafar, F., Akram, M.: A novel decision-making method based on rough fuzzy information. Int. J. Fuzzy Syst. 20(3), 1000–1014 (2018)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, 4590, Pakistan

    Tahira Batool & Uzma Ahmad

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  1. Tahira Batool
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  2. Uzma Ahmad
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UA, TB; Investigation and writing original draft of research work, TB; Writing review and editing.

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Correspondence to Uzma Ahmad.

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Batool, T., Ahmad, U. A new approximation technique based on central bodies of rough fuzzy directed graphs for agricultural development. J. Appl. Math. Comput. 70, 1673–1705 (2024). https://doi.org/10.1007/s12190-024-02032-4

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  • DOI: https://doi.org/10.1007/s12190-024-02032-4

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