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Multi-Granularity Probabilistic Rough Fuzzy Sets for Interval-Valued Fuzzy Decision Systems

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Abstract

The probabilistic rough set (PRS) model, through the incorporation of error levels, represents a quantitative extension of the classical rough set model. It serves as a fundamental expansion that enables robust fault tolerance capabilities by employing relative quantitative description. However, when confronted with interval-valued fuzzy data, the PRS model is rendered ineffective. The primary reason for this lies in the absence of a unique equivalence relation in interval-valued decision systems. This paper presents a novel approach to address this limitation. In this paper, we first propose a fuzzy similarity relation based on diversity function, which establishes a viable foundation for constricting models of probabilistic rough fuzzy set and multi-granularity probabilistic rough set models for interval-valued fuzzy decision systems. Then the decision rules are derived from the presented three kinds of multi-granularity probabilistic rough fuzzy sets, respectively. In order to elucidate the concepts of interval-valued probabilistic rough fuzzy sets and multi-granularity probabilistic rough fuzzy sets, a case study is considered, which is helpful for applying these theories to deal with practical issues.

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References

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

    Article  MATH  Google Scholar 

  2. Li, W., Zhou, H., Xu, W., Wang, X.Z., Pedrycz, W.: Interval dominance-based feature selection for interval-valued ordered data. IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3184120

    Article  Google Scholar 

  3. Kowalski, P.A., Jeczmionek, E.: Parallel complete gradient clustering algorithm and its properties. Inf. Sci. 600, 155–169 (2022)

    Article  Google Scholar 

  4. Gupta, A., Das, S.: On efficient model selection for sparse hard and fuzzy center-based clustering algorithms. Inf. Sci. 590, 29–44 (2022)

    Article  Google Scholar 

  5. Lee, C., Lee, G.G.: Information gain and divergence-based feature selection for machine learning-based text categorization. Inform. Process. Manag. 42, 155–165 (2006)

    Article  Google Scholar 

  6. Leung, Y., Fischer, M., Wu, W., Mi, J.: A rough set approach for the discovery of classification rules in interval-valued information systems. Int. J. Approx. Reason. 47(2), 233–246 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Huang, B., Wei, D., Li, H., Zhuang, Y.: Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems. Inf. Sci. 221, 215–229 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pan, Y., Wu, Y., Lam, H.K.: Security-based fuzzy control for nonlinear networked control systems with DoS attacks via a resilient event-triggered scheme. IEEE Trans. Fuzzy Syst. 30(10), 4359–4368 (2022)

    Article  Google Scholar 

  9. Wang, C., Qi, Y., Shao, M., Hu, Q., Chen, D., Qian, Y., Lin, Y.: A fitting model for feature selection with fuzzy rough sets. IEEE Trans. Fuzzy Syst. 25(4), 741–753 (2008)

    Article  Google Scholar 

  10. Dai, J., Wang, W., Mi, J.: Uncertainty measurement for interval-valued information systems. Inf. Sci. 251, 63–78 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lin, Y., Hu, Q., Liu, J., Li, J., Wu, X.: Streaming feature selection for multilabel learning based on fuzzy mutual information. IEEE Trans. Fuzzy Syst. 25(6), 1491–1507 (2017)

    Article  Google Scholar 

  12. Hosseini, S.M., Paydar, M.M., Keshteli, M.H.: Recovery solutions for ecotourism centers during the Covid-19 pandemic: utilizing fuzzy DEMATEL and fuzzy VIKOR methods. Expert Syst. Appl. 185, 115594 (2021)

    Article  Google Scholar 

  13. Querales, M., Salas, R., Morales, Y., Allende-Cid, H., Rosas, H.: A stacking neuro-fuzzy framework to forecast runoff from distributed meteorological stations. Appl. Soft Comput. 118, 108535 (2022)

    Article  Google Scholar 

  14. Versaci, M., Morabito, F.C.: Image edge detection: a new approach based on fuzzy entropy and fuzzy divergence. Int. J. Fuzzy Syst. 23(4), 918–936 (2021)

    Article  Google Scholar 

  15. Xiao, F.: CaFtR: a fuzzy complex event processing method. Int. J. Fuzzy Syst. 24(2), 1098–1111 (2022)

    Article  MathSciNet  Google Scholar 

  16. Xie, D., Xiao, F., Pedrycz, W.: Information quality for intuitionistic fuzzy values with its application in decision making. Eng. Appl. Artif. Intell. 109, 104568 (2022)

    Article  Google Scholar 

  17. Ghosh, A., Mishra, N.S., Ghosh, S.: Fuzzy clustering algorithms for unsupervised change detection in remote sensing images. Inf. Sci. 181(4), 699–715 (2011)

    Article  Google Scholar 

  18. Pawlak, Z.: Rough sets. J. Comput. Inf. sci. 11, 341–356 (1982)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  20. Dai, J., Hu, H., Wu, W.Z., Qian, Y., Huang, D.: Maxmal-discernibility-pair-based approach to attribute reduction in fuzzy rough sets. IEEE Trans. Fuzzy Syst. 26(4), 2174–2187 (2017)

    Article  Google Scholar 

  21. Yang, Y., Chen, D., Wang, H., Wang, X.: Incremental perspective for feature selection based on fuzzy rough sets. IEEE Trans. Fuzzy Syst. 26(3), 1257–1273 (2018)

    Article  Google Scholar 

  22. Wang, C., Huang, Y., Shao, M., Fan, X.: Fuzzy rough set-based attribute reduction using distance measures. Knowl.-Based Syst. 164, 205–212 (2019)

    Article  Google Scholar 

  23. Yang, X., Zhang, M.: Dominance-based fuzzy rough approach to an interval-valued decision system. Front. Comput. Sci. 5(2), 195–204 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yao, Y.: Probabilistic rough set approximations. Int. J. Approx. Reason. 49(2), 255–271 (2008)

    Article  MATH  Google Scholar 

  25. Yao, Y.: The superiority of three-way decisions in probabilistic rough set models. Inf. Sci. 181, 1080–1096 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Yao, Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180, 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  27. Yao, Y.: Information granulation and rough set approximation. Int. J. Intell. Syst. 16, 87–104 (2001)

    Article  MATH  Google Scholar 

  28. Peters, J.F., Pawlak, Z., Skowron, A.: A rough set approach to measuring information granules. Comput. Softw. Appl. Conf. pp. 1135-1139, (2002)

  29. Rasiowa, H.: Mechanical proof systems for logic: reaching consensus by groups of intelligent systems. Int. J. Approx. Reason. 5(4), 415–432 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  30. Qian, Y., Liang, J.: Rough set method based on multi-granulations In: Proc. 5th IEEE Conf. Cogn. Inf., vol. 1, pp. 297-304, (2006)

  31. Li, W., Xu, W., Zhang, X., Zhang, J.: Updating approximations with dynamic objects based on local multigranulation rough sets in ordered information systems. Artif. Intell. Rev. 55(8), 1821–1855 (2021)

    Google Scholar 

  32. Mandal, P., Ranadive, A.S.: Fuzzy multigranulation decision-theoretic rough sets based on fuzzy preference relation. Soft Comput. 23(1), 85–99 (2019)

    Article  MATH  Google Scholar 

  33. Qian, Y., Liang, X., Lin, G., Guo, Q., Liang, J.: Local multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 82, 119–137 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  34. Zhou, H., Li, W., Zhang, C., Zhan, T.: Dynamic maintenance of approximations based on dominance-based rough set approach in interval-valued information system. Appl. Intell. (2023). https://doi.org/10.1007/s10489-023-04655-9

    Article  Google Scholar 

  35. Wang, Z., Xiao, F., Ding, W.: Interval-valued intuitionistic fuzzy jenson-shannon divergence and its application in multi-attribute decision making. Appl. Intell. 52, 16168–16184 (2022)

    Article  Google Scholar 

  36. Liu, J., Huang, B., Li, H., Bu, X., Zhou, X.: Optimization-based three-way decisions with interval-valued intuitionistic fuzzy information. IEEE Trans. Cyb. 53(6), 3829–3843 (2023)

    Article  Google Scholar 

  37. Sun, L., Zhu, L., Li, W., Zhang, Ch., Balezentis, T.: Interval-valued functional clustering based on the Wasserstein distance with application to stock data. Inf. Sci. 606, 910–926 (2022)

    Article  Google Scholar 

  38. Rico, N., Huidobro, P., Bouchet, A., Diaz, I.: Similarity measures for interval-valued fuzzy sets based on average embeddings and its application to hierarchical clustering. Inf. Sci. 615, 794–812 (2022)

    Article  Google Scholar 

  39. Yang, L., Qin, K., Sang, B., Xu, W.: Dynamic maintenance of variable precision fuzzy neighborhood three-way regions in interval-valued fuzzy decision system. Int. J. Mach. Learn. Cybern. 13, 1797–1818 (2022)

    Article  Google Scholar 

  40. Du, C., Ye, J.: Decision-making strategy for slope stability using similarity measures between interval-valued fuzzy credibility sets. Soft Comput. 26, 5105–5114 (2022)

    Article  Google Scholar 

  41. Zhang, X., Li, J.: Incremental feature selection approach to interval-valued fuzzy decision information systems based on \(\lambda\)-fuzzy similarity self-information. Inf. Sci. 625, 593–619 (2023)

    Article  Google Scholar 

  42. Chang, W., Fu, C., Chang, L.: Triangular bounded consistency of interval-valued fuzzy preference relations. IEEE Trans. Fuzz. Syst. 30(12), 5511–5525 (2022)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the Associate Editor and the reviewers for their insightful comments and suggestions.

Funding

This paper is supported by the National Natural Science Foundation of China (No. 12201518), the China Postdoctoral Science Foundation (No. 2023T160401), the Natural Science Foundation of Chongqing (No. CSTB2023NSCQ-MSX0152), the Science and Technology Research Program of Chongqing Education Commission (Nos. KJQN202300202, KJQN202100205, KJQN202100206).

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Authors and Affiliations

  1. College of Artificial Intelligence, Southwest University, Chongqing, 400715, People’s Republic of China

    Wentao Li

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Tao Zhan

  3. The School of Automation, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Tao Zhan

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  1. Wentao Li
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Correspondence to Tao Zhan.

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Li, W., Zhan, T. Multi-Granularity Probabilistic Rough Fuzzy Sets for Interval-Valued Fuzzy Decision Systems. Int. J. Fuzzy Syst. 25, 3061–3073 (2023). https://doi.org/10.1007/s40815-023-01577-z

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