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AIMS Mathematics

2026, Volume 11, Issue 3: 8065-8103. doi: 10.3934/math.2026332
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Advancements in intuitionistic fuzzy rough graphs

  • 1.
    College of Accounting, Guangzhou College of Technology and Business, Guangzhou 528138, China
  • 2.
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
  • 3.
    Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
  • Published: 26 March 2026

  • MSC : 03E72, 05C72, 05C99, 57M15

  • Rough sets and intuitionistic fuzzy (IF) sets are two separate mathematical frameworks designed to model and manage incomplete or uncertain knowledge. By integrating these models, an IF rough framework is constructed, offering enhanced expressiveness and flexibility for representing and processing incomplete data within information systems. In this paper, we introduce a new hybrid model utilizing minimal IF neighborhoods. This model, based on any two IF binary relations defined on a non-empty universe, leads to the development of two novel IF graph approximation spaces aimed at reducing the boundary region of fuzzy uncertainty and increasing the precision degree of the fuzzy approximations. Furthermore, key results pertaining to both types of IF graph approximations are established. The relationships between the existing IF approximation methods are derived, and comparisons are made to demonstrate that the proposed approaches are more general than previous models. Finally, we explore an application of these IF graph approximation spaces in decision-making contexts and propose an algorithm to facilitate solving such problems.

    Citation: Dali Shi, Salah E. Abbas, Hossam M. Khiamy, Ismail Ibedou. Advancements in intuitionistic fuzzy rough graphs[J]. AIMS Mathematics, 2026, 11(3): 8065-8103. doi: 10.3934/math.2026332

    Related Papers:

  • Rough sets and intuitionistic fuzzy (IF) sets are two separate mathematical frameworks designed to model and manage incomplete or uncertain knowledge. By integrating these models, an IF rough framework is constructed, offering enhanced expressiveness and flexibility for representing and processing incomplete data within information systems. In this paper, we introduce a new hybrid model utilizing minimal IF neighborhoods. This model, based on any two IF binary relations defined on a non-empty universe, leads to the development of two novel IF graph approximation spaces aimed at reducing the boundary region of fuzzy uncertainty and increasing the precision degree of the fuzzy approximations. Furthermore, key results pertaining to both types of IF graph approximations are established. The relationships between the existing IF approximation methods are derived, and comparisons are made to demonstrate that the proposed approaches are more general than previous models. Finally, we explore an application of these IF graph approximation spaces in decision-making contexts and propose an algorithm to facilitate solving such problems.



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    [1] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (1982), 341–356. https://doi.org/10.1007/BF01001956
    [2] S. H. Nguyen, A. Skowron, P. Synak, Discovery of data patterns with applications to decomposition and classification problems, In: Rough sets in knowledge discovery 2, Berlin Heidelberg: Springer, 1998, 55–97. https://doi.org/10.1007/978-3-7908-1883-3_4
    [3] Z. Pawlak, A. Skowron, Rough sets and Boolean reasoning, Inform. Sciences, 177 (2007), 41–73. https://doi.org/10.1016/j.ins.2006.06.007 doi: 10.1016/j.ins.2006.06.007
    [4] Z. Pawlak, A. Skowron, Rudiments of rough sets, Inform. Sciences, 177 (2007), 3–27. https://doi.org/10.1016/j.ins.2006.06.003
    [5] Z. Pei, D. W. Pei, L. Zheng, Topology vs generalized rough sets, Int. J. Approx. Reason., 52 (2011), 231–239. https://doi.org/10.1016/j.ijar.2010.07.010 doi: 10.1016/j.ijar.2010.07.010
    [6] S. E. Abbas, H. M. Khiamy, E. El-Sanowsy, New approach for closure spaces by relations via ideals, Annals of Fuzzy Mathematics and Informatics, 26 (2023), 59–81. https://doi.org/10.30948/afmi.2023.26.1.59 doi: 10.30948/afmi.2023.26.1.59
    [7] E. Kay, Graph theory with applications, J. Oper. Res. Soc., 28 (1977), 237–238. http://doi.org/10.1057/jors.1977.45 doi: 10.1057/jors.1977.45
    [8] S. Nada, A. E. F. El-Atik, M. Atef, New types of topological structures via graphs, Math. Method. Appl. Sci., 41 (2018), 5801–5810. https://doi.org/10.1002/mma.4726 doi: 10.1002/mma.4726
    [9] D. L. Shi, S. E. Abbas, H. M. Khiamy, I. Ibedou, On graph primal topological spaces, Axioms, 14 (2025), 662. https://doi.org/10.3390/axioms14090662 doi: 10.3390/axioms14090662
    [10] R. Alharbi, S. E. D. Abbas, H. M. O. Khiamy, I. Ibedou, New approach for closure spaces on graphs based on relations and graph ideals, Axioms, 14 (2025), 886. https://doi.org/10.3390/axioms14120886 doi: 10.3390/axioms14120886
    [11] D. L. Shi, S. E. Abbas, H. M. Khiamy, I. Ibedou, Fuzzy rough graphs via fuzzy graph ideals with applications, AIMS Math., 11 (2026), 2979–3007. https://doi.org/10.3934/math.2026119 doi: 10.3934/math.2026119
    [12] L. Q. Li, C. Z. Jia, X. R. Li, A novel intuitionistic fuzzy VIKOR method to MCDM based on intuitionistic fuzzy $\beta^*$-covering rough set, Expert Syst. Appl., 293 (2025), 128713. https://doi.org/10.1016/j.eswa.2025.128713 doi: 10.1016/j.eswa.2025.128713
    [13] H. Y. Zheng, C. X. Bo, L. Q. Li, L. Wang, W. J. Jiang, A novel multi-granularity variable precision neutrosophic rough set and group decision-making application with three strategies, AIMS Math., 10 (2025), 23187–23219. https://doi.org/10.3934/math.20251029 doi: 10.3934/math.20251029
    [14] A. Rosenfeld, Fuzzy graph, In: Fuzzy sets and their applications to cognitive and decision process, New York: Academic Press, 1975, 77–95. https://doi.org/10.1016/B978-0-12-775260-0.50008-6
    [15] A. Kaufmann, Introduction à la théorie des sous-ensembles flous, Paris: Masson et Cie, 1973.
    [16] L. A. Zadeh, Similarity relations and fuzzy orderings, Inform. Sciences, 3 (1971), 177–200. https://doi.org/10.1016/S0020-0255(71)80005-1 doi: 10.1016/S0020-0255(71)80005-1
    [17] R. Slowinski, D. Vanderpooten, A generalized definition of rough approximations based on similarity, IEEE Trans. Knowl. Data Eng., 12 (2000), 331–336. https://doi.org/10.1109/69.842271 doi: 10.1109/69.842271
    [18] Z. S. Mufti, A. Tabraiz, Q. Xin, B. Almutairi, R. Anjum, Fuzzy topological analysis of pizza graph, AIMS Math., 8 (2023), 12841–12856. https://doi.org/10.3934/math.2023647 doi: 10.3934/math.2023647
    [19] M. Akram, M. Arshad, Shumaiza, Fuzzy rough graph theory with applications, Int. J. Comput. Intell. Syst., 12 (2018), 90–107. https://doi.org/10.2991/ijcis.2018.25905184 doi: 10.2991/ijcis.2018.25905184
    [20] M. Akram, F. Zafar, Rough fuzzy digraphs with application, J. Appl. Math. Comput., 59 (2019), 91–127. https://doi.org/10.1007/s12190-018-1171-2 doi: 10.1007/s12190-018-1171-2
    [21] H. M. Malik, M. Akram, A new approach based on intuitionistic fuzzy rough graphs for decision-making, J. Intell. Fuzzy Syst., 34 (2018), 2325–2342. https://doi.org/10.3233/JIFS-171395 doi: 10.3233/JIFS-171395
    [22] R. Parvathi, M. G. Karunambigai, K. T. Atanassov, Operations on intuitionistic fuzzy graphs, In: 2009 IEEE international conference on fuzzy systems, Jeju, Korea (South), 2009, 1396–1401. https://doi.org/10.1109/FUZZY.2009.5277067
    [23] J. M. Zhan, H. M. Malik, M. Akram, Novel decision-making algorithms based on intuitionistic fuzzy rough environment, Int. J. Mach. Learn. Cybern., 10 (2019), 1459–1485. https://doi.org/10.1007/s13042-018-0827-4 doi: 10.1007/s13042-018-0827-4
    [24] N. Shaik, S. B. Shaik, Wiener index application in intuitionistic fuzzy rough graphs for transport network flow, Sci. Rep., 15 (2025), 9591. https://doi.org/10.1038/s41598-025-94488-y doi: 10.1038/s41598-025-94488-y
    [25] A. A. Allam, M. Y. Bakeir, E. A. Abo-Tabl, New approach for closure spaces by relations, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 22 (2006), 285–304.
    [26] A. Kandil, M. M. Yakout, A. Zakaria, Generalized rough sets via ideals, Annals of Fuzzy Mathematics and Informatics, 5 (2013), 525–532.
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