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Granular-Ball Three-Way Decision

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Rough Sets (IJCRS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14481))

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Abstract

By thinking, information processing and decision-making in threes, the idea, theory and methods of three-way decision have been successfully applied to various domains. However, the current three-way decision has two following limitations. On the one hand, the narrow three-way decision associated with rough sets either has trouble processing continuous data or fails to represent knowledge by equivalence classes. On the other hand, the inputs of generalized three-way decision are individual objects rather than equivalence classes, which reduces the decision efficiency. To this end, we try to integrate efficient granular-ball computing into three-way decision. Firstly, we propose a novel model, i.e., granular-ball three-way decision to improve the efficiency and robustness of three-way decision. Secondly, sequential three-way decision based on granular-ball is presented to investigate the appropriate multi-granularity structures and represent the same object at different granularities. Finally, we analyze the advantages of granular-balls to strengthen the real-world applications of three-way decision.

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References

  1. Campagner, A., Cabitza, F., Ciucci, D.: Three-way decision for handling uncertainty in machine learning: a narrative review. In: Bello, R., Miao, D., Falcon, R., Nakata, M., Rosete, A., Ciucci, D. (eds.) IJCRS 2020. LNCS (LNAI), vol. 12179, pp. 137–152. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-52705-1_10

    Chapter  Google Scholar 

  2. Chen, L.: Topological structure in visual perception. Science 218(4573), 699–700 (1982)

    Article  Google Scholar 

  3. Chen, Y., Wang, P., Yang, X., Mi, J., Liu, D.: Granular ball guided selector for attribute reduction. Knowl.-Based Syst. 229, 107326 (2021)

    Article  Google Scholar 

  4. Fang, Y., Cao, X.M., Wang, X., Min, F.: Three-way sampling for rapid attribute reduction. Inf. Sci. 609, 26–45 (2022)

    Article  Google Scholar 

  5. Han, X.Y., Zhu, X.B., Pedrycz, W., Li, Z.W.: A three-way classification with fuzzy decision trees. Appl. Soft Comput. 132, 109788 (2023)

    Article  Google Scholar 

  6. Hua, H.Q., Ren, Y.D., Xia, X.Z.: Numerical attribute reduction based on neighborhood granulation and rough approximation. J. Softw. 19(3), 640–649 (2008)

    Article  Google Scholar 

  7. Huang, C.C., Li, J.H., Mei, C.L., Wu, W.Z.: Three-way concept learning based on cognitive operators: an information fusion viewpoint. Int. J. Approx. Reason. 83, 218–242 (2017)

    Article  MathSciNet  Google Scholar 

  8. Li, H.X., Zhang, L.B., Huang, B., Zhou, X.Z.: Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl.-Based Syst. 91, 241–251 (2016)

    Article  Google Scholar 

  9. Li, W., Yang, B.: Three-way decisions with fuzzy probabilistic covering-based rough sets and their applications in credit evaluation. Appl. Soft Comput. 136, 110144 (2023)

    Article  Google Scholar 

  10. Maldonado, S., Peters, G., Weber, R.: Credit scoring using three-way decisions with probabilistic rough sets. Inf. Sci. 507, 700–714 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Qian, W., Xu, F., Huang, J., Qian, J.: A novel granular ball computing-based fuzzy rough set for feature selection in label distribution learning. Knowl.-Based Syst. 278, 110898 (2023)

    Article  Google Scholar 

  13. Shah, A., Ali, B., Habib, M., Frnda, J., Ullah, I., Anwar, M.S.: An ensemble face recognition mechanism based on three-way decisions. J. King Saud Univ.-Comput. Inf. Sci. 35(4), 196–208 (2023)

    Google Scholar 

  14. Shu Yin, X., Da Wei, D., Long, Y., Li, Z., Danf, L., Guoy, W., et al.: Graph-based representation for image based on granular-ball. arXiv preprint arXiv:2303.02388 (2023)

  15. Song, M., Chen, J., Song, J., Xu, T., Fan, Y.: Forward greedy searching to \(\kappa \)-reduct based on granular ball. Symmetry 15(5), 996 (2023)

    Article  Google Scholar 

  16. Wang, G.Y.: DGCC: data-driven granular cognitive computing. Granul. Comput. 2(4), 343–355 (2017)

    Article  Google Scholar 

  17. Wang, P.X., Yao, Y.Y.: CE3: a three-way clustering method based on mathematical morphology. Knowl.-Based Syst. 155, 54–65 (2018)

    Article  Google Scholar 

  18. Wang, W.J., Zhan, J.M., Zhang, C., Herrera-Viedma, E., Kou, G.: A regret-theory-based three-way decision method with a priori probability tolerance dominance relation in fuzzy incomplete information systems. Inf. Fusion 89, 382–396 (2023)

    Article  Google Scholar 

  19. Wang, X.H., Wang, B., Liu, S., Li, H.X., Wang, T.X., Watada, J.: Fuzzy portfolio selection based on three-way decision and cumulative prospect theory. Int. J. Mach. Learn. Cybernet. 13(1), 293–308 (2022)

    Article  Google Scholar 

  20. Xia, S.Y., Dai, X.C., Wang, G.Y., Gao, X.B., Giem, E.: An efficient and adaptive granular-ball generation method in classification problem. IEEE Trans. Neural Netw. Learn. Syst. 1–13 (2022)

    Google Scholar 

  21. Xia, S.Y., Liu, Y.S., Ding, X., Wang, G.Y., Yu, H., Luo, Y.G.: Granular ball computing classifiers for efficient, scalable and robust learning. Inf. Sci. 483, 136–152 (2019)

    Article  MathSciNet  Google Scholar 

  22. Xia, S.Y., et al.: A unified granular-ball learning model of Pawlak rough set and neighborhood rough set. arXiv preprint arXiv:2201.03349 (2022)

  23. Xia, S.Y., Wang, G.Y., Gao, X.B., Peng, X.L.: GBSVM: granular-ball support vector machine. arXiv preprint arXiv:2210.03120 (2022)

  24. Xia, S.Y., Zheng, S.Y., Wang, G.Y., Gao, X.B., Wang, B.G.: Granular ball sampling for noisy label classification or imbalanced classification. IEEE Trans. Neural Netw. Learn. Syst. 34, 2144–2155 (2021)

    Article  Google Scholar 

  25. Xie, J., Kong, W.Y., Xia, S.Y., Wang, G.Y., Gao, X.B.: An efficient spectral clustering algorithm based on granular-ball. IEEE Trans. Knowl. Data Eng. 35, 9743–9753 (2023)

    Article  Google Scholar 

  26. Xie, J., Xia, S.Y., Wang, G.Y., Gao, X.B.: GBMST: an efficient minimum spanning tree clustering based on granular-ball. arXiv e-prints, pp. arXiv–2303 (2023)

    Google Scholar 

  27. Yang, X., Li, Y.H., Li, T.R.: A review of sequential three-way decision and multi-granularity learning. Int. J. Approx. Reason. 152, 414–433 (2022)

    Article  MathSciNet  Google Scholar 

  28. Yang, X., Li, Y.J., Liu, D., Li, T.R.: Hierarchical fuzzy rough approximations with three-way multigranularity learning. IEEE Trans. Fuzzy Syst. 30(9), 3486–3500 (2021)

    Article  Google Scholar 

  29. Yang, X., Li, Y.J., Meng, D., Yang, Y.X., Liu, D., Li, T.R.: Three-way multi-granularity learning towards open topic classification. Inf. Sci. 585, 41–57 (2022)

    Article  Google Scholar 

  30. Yang, X., Loua, M.A., Wu, M.J., Huang, L., Gao, Q.: Multi-granularity stock prediction with sequential three-way decisions. Inf. Sci. 621, 524–544 (2023)

    Article  Google Scholar 

  31. Yao, Y.: Three-way decision: an interpretation of rules in rough set theory. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.) RSKT 2009. LNCS (LNAI), vol. 5589, pp. 642–649. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02962-2_81

    Chapter  Google Scholar 

  32. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180(3), 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  33. Yao, Y.: Granular computing and sequential three-way decisions. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013. LNCS (LNAI), vol. 8171, pp. 16–27. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41299-8_3

    Chapter  Google Scholar 

  34. Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Int. J. Man Mach. Stud. 37(6), 793–809 (1992)

    Article  Google Scholar 

  35. Yao, Y.Y., Yang, J.L.: Granular fuzzy sets and three-way approximations of fuzzy sets. Int. J. Approx. Reason. 161, 109003 (2023)

    Article  MathSciNet  Google Scholar 

  36. Ye, X.Q., Liu, D., Li, T.R.: Multi-granularity sequential three-way recommendation based on collaborative deep learning. Int. J. Approx. Reason. 152, 434–455 (2023)

    Article  MathSciNet  Google Scholar 

  37. Yu, H.: Three-way decisions and three-way clustering. In: Nguyen, H.S., Ha, Q.-T., Li, T., Przybyła-Kasperek, M. (eds.) IJCRS 2018. LNCS (LNAI), vol. 11103, pp. 13–28. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99368-3_2

    Chapter  Google Scholar 

  38. Zhong, Y.H., Li, Y.H., Yang, Y., Li, T., Jia, Y.L.: An improved three-way decision model based on prospect theory. Int. J. Approx. Reason. 142, 109–129 (2022)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the Natural Science Foundation of Sichuan Province (No. 2022NSFSC0528), the Sichuan Science and Technology Program (No. 2022ZYD0113), Jiaozi Institute of Fintech Innovation, Southwestern University of Finance and Economics (Nos. kjcgzh20230103, kjcgzh20230201), the Fundamental Research Funds for the Central Universities (No. JBK2307055).

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Authors and Affiliations

  1. School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Xin Yang & Yanhua Li

  2. Chongqing Key Laboratory of Computational Intelligence, Key Laboratory of Big Data Intelligent Computing, Key Laboratory of Cyberspace Big Data Intelligent Security, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Shuyin Xia, Xiaoyu Lian & Guoyin Wang

  3. School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, 611756, China

    Tianrui Li

Authors
  1. Xin Yang
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  2. Yanhua Li
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  3. Shuyin Xia
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  4. Xiaoyu Lian
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  5. Guoyin Wang
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  6. Tianrui Li
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Corresponding author

Correspondence to Xin Yang .

Editor information

Editors and Affiliations

  1. IRCCS Istituto Ortopedico Galeazzi, Milano, Italy

    Andrea Campagner

  2. Ghent University, Ghent, Belgium

    Oliver Urs Lenz

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Shuyin Xia

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. AGH University of Science and Technology, Kraków, Poland

    Jarosław Wąs

  6. University of Regina, Regina, SK, Canada

    JingTao Yao

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Yang, X., Li, Y., Xia, S., Lian, X., Wang, G., Li, T. (2023). Granular-Ball Three-Way Decision. In: Campagner, A., Urs Lenz, O., Xia, S., Ślęzak, D., Wąs, J., Yao, J. (eds) Rough Sets. IJCRS 2023. Lecture Notes in Computer Science(), vol 14481. Springer, Cham. https://doi.org/10.1007/978-3-031-50959-9_20

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  • DOI: https://doi.org/10.1007/978-3-031-50959-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-50958-2

  • Online ISBN: 978-3-031-50959-9

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