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The Visual Analysis of Three-Way Decision Based on Decision-Theoretic Rough Set: A Perspective of Fusing Two-Way Decision Pair

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Rough Sets (IJCRS 2024)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14840))

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Abstract

Three-way decisions (3WDs) based on decision-theoretic rough set (DTRS), as a crucial theory in the field of granular computing, have received extensive attention. Meanwhile, visualization technologies have gained popularity, particularly for their intuitiveness and explainability. In order to understand the basic theory of 3WD more intuitively and enhance the interpretability analysis of threshold, this paper proposes the visual analysis of 3WD based on DTRS using the perspective of fusing two-way decision (2WD) pair. Firstly, the p-r space is defined via the geometric interpretations of the Bayesian decision procedure. Secondly, we propose a pair of 2WDs, i.e., the 2WD with acceptance and non-acceptance and the 2WD with rejection and non-rejection. And their geometrical interpretations are discussed in p-r space. Then, a fusing of the 2WD pair is proposed, and the geometric relations between its threshold and loss function are analyzed in p-r space. Finally, degeneration in the 2WD pair into the 3WD is obtained via the special loss function, which is employed to get the geometric interpretations for the threshold and loss function of single-evaluation-based 3WDs in p-r space. The method proposed in this paper uses the p-r space to obtain more intuitive explainability, which is more easily interpreted and reasoned of 3WD and has greater potential for generalization.

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References

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

    Article  Google Scholar 

  2. Pawlak, Z.: Some issues on rough sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27794-1_1

    Chapter  Google Scholar 

  3. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data, vol. 9. Springer, Dordrecht (2012). https://doi.org/10.1007/978-94-011-3534-4

    Book  Google Scholar 

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

    Article  Google Scholar 

  5. Yao, Y.: Decision-theoretic rough set models. In: Yao, J.T., Lingras, P., Wu, W.-Z., Szczuka, M., Cercone, N.J., Ślȩzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 1–12. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72458-2_1

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Yao, Y.: Rough sets and three-way decisions. In: Ciucci, D., Wang, G., Mitra, S., Wu, W.-Z. (eds.) RSKT 2015. LNCS (LNAI), vol. 9436, pp. 62–73. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25754-9_6

    Chapter  Google Scholar 

  8. Zou, D.D., Xu, Y.L., Li, L.Q., et al.: Novel variable precision fuzzy rough sets and three-way decision model with three strategies. Inf. Sci. 629, 222–248 (2023)

    Article  Google Scholar 

  9. Stepaniuk, J., Skowron, A.: Three-way approximation of decision granules based on the rough set approach. Int. J. Approximate Reasoning 155, 1–16 (2023)

    Article  MathSciNet  Google Scholar 

  10. Zou, D., Xu, Y., Li, L., et al.: Novel variable precision fuzzy rough sets and three-way decision model with three strategies. Inf. Sci. 629, 222–248 (2023)

    Article  Google Scholar 

  11. Li, R., Yang, J., Zhang, X.: Optimal scale selection based on three-way decisions with decision-theoretic rough sets in multi-scale set-valued decision tables. Int. J. Mach. Learn. Cybern. 14(11), 3719–3736 (2023)

    Article  Google Scholar 

  12. Liu, F., Liu, Y., Abdullah, S.: Three-way decisions with decision-theoretic rough sets based on covering-based q-rung orthopair fuzzy rough set model. J. Intell. Fuzzy Syst. 40(5), 9765–9785 (2021)

    Article  Google Scholar 

  13. Wang, N., Zhu, P.: A three-way decision model associated with decision-theoretic rough fuzzy sets based on computing with words. J. Intell. Fuzzy Syst. 45(1), 285–304 (2023)

    Article  Google Scholar 

  14. Guo, C., Yu, Z.H., Wu, S.Y., et al.: A three-way decision approach combining probabilistic and decision-theoretic rough set. In: International Conference on Computer and Information Science, pp. 296–301 (2022)

    Google Scholar 

  15. Ali, Z., Mahmood, T., Khan, M.B.: Three-way decisions with complex q-rung orthopair 2-tuple linguistic decision-theoretic rough sets based on generalized Maclaurin symmetric mean operators. AIMS Math. 8(8), 17943–17980 (2023)

    Article  Google Scholar 

  16. Zhang, H.D., Ma, Q.: Three-way decisions with decision-theoretic rough sets based on Pythagorean fuzzy covering. Soft. Comput. 24(24), 18671–18688 (2020)

    Article  Google Scholar 

  17. Abdullah, S., Al-Shomrani, M.M., Liu, P., et al.: A new approach to three-way decisions making based on fractional fuzzy decision-theoretical rough set. Int. J. Intell. Syst. 37(3), 2428–2457 (2022)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J.T., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1–17. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32115-3_1

    Chapter  Google Scholar 

  20. Li, B., Tian, L.Y., Han, Y., et al.: Three-way decision of target threat decision making based on adaptive threshold algorithms. J. Eng. 2020(13), 293–297 (2020)

    Google Scholar 

  21. Li, Y.S., Shao, X.Y.: Thresholds learning of three-way decisions in pairwise crime linkage. Appl. Soft Comput. 120, 108638 (2022)

    Article  Google Scholar 

  22. Yang, J., Zhang, G.M.: Dynamic dual-threshold virtual machine merging method based on three-way decision. Symmetry 14(9), 1865 (2022)

    Article  Google Scholar 

  23. Liu, J.B., Hu, S.L., Li, H.X., et al.: Achieving threshold consistency in three-way group decision using optimization methodology and expert-weight-updating-strategy. Int. J. Approximate Reasoning 158, 108922 (2023)

    Article  MathSciNet  Google Scholar 

  24. Muntwiler, C., Eppler, M.J.: Improving decision making through visual knowledge calibration. Manag. Decis. 61(8), 2374–2390 (2023)

    Article  Google Scholar 

  25. Saito, T., Sudo, R., Takano, Y.: The gaze bias effect in toddlers: preliminary evidence for the developmental study of visual decision-making. Dev. Sci. 23(6), e12969 (2020)

    Article  Google Scholar 

  26. Xu, J.F., Miao, D.Q., Zhang, L., et al.: Algebraic formulations and geometric interpretations of decision-theoretic rough sets. In: Campagner, A., Urs Lenz, O., Xia, S., Ślȩzak, D., Was, J., Yao, J. (eds.) IJCRS 2023. LNCS, vol. 14481, pp. 31–45. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-50959-9_3

  27. Germar, M., Duderstadt, V.H., Mojzisch, A.: Social norms shape visual appearance: taking a closer look at the link between social norm learning and perceptual decision-making. Cognition 241, 105611 (2023)

    Article  Google Scholar 

  28. Bleichman, I., Yadav, P., Ayali, A.: Visual processing and collective motion-related decision-making in desert locusts. Proc. R. Soc. B 290, 20221862 (2023)

    Article  Google Scholar 

  29. Widyatama, A., Narsa, I.M.: The use of visual presentations for integrated reports in the investment decision-making process. J. Appl. Acc. Res. 24(1), 106–133 (2023)

    Google Scholar 

  30. Hu, M.: Three-way data analytics: preparing and analyzing data in threes. Inf. Sci. 573, 412–432 (2021)

    Article  MathSciNet  Google Scholar 

  31. Xu, J.F., Zhang, Y.J., Miao, D.Q.: Three-way confusion matrix for classification: a measure driven view. Inf. Sci. 507, 772–794 (2020)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported in National Natural Science Foundations of China (Grant No. 62266032), Jiangxi Training Program for Academic and Technical Leaders in Major Disciplines-Leading Talents Project (Grant No. 20225BCI22016).

Author information

Authors and Affiliations

  1. School of Software, Nanchang University, Nanchang, 330047, Jiangxi, China

    Jing Tu, Hong Rao & Jianfeng Xu

  2. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Songjiang, Shanghai, 201620, China

    Jing Tu

  3. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, China

    Duoqian Miao

  4. China UnionPay Co., Ltd., Shanghai, 201201, China

    Yuanjian Zhang

Authors
  1. Jing Tu
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  2. Hong Rao
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  3. Jianfeng Xu
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  4. Duoqian Miao
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  5. Yuanjian Zhang
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Corresponding authors

Correspondence to Jianfeng Xu or Duoqian Miao .

Editor information

Editors and Affiliations

  1. Saint Mary's University, halifax, NS, Canada

    Mengjun Hu

  2. Ghent University, Ghent, Belgium

    Chris Cornelis

  3. California State University, San Bernardino, CA, USA

    Yan Zhang

  4. Saint Mary's University, Halifax, NS, Canada

    Pawan Lingras

  5. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  6. University of Regina, Regina, SK, Canada

    JingTao Yao

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Tu, J., Rao, H., Xu, J., Miao, D., Zhang, Y. (2024). The Visual Analysis of Three-Way Decision Based on Decision-Theoretic Rough Set: A Perspective of Fusing Two-Way Decision Pair. In: Hu, M., Cornelis, C., Zhang, Y., Lingras, P., Ślęzak, D., Yao, J. (eds) Rough Sets. IJCRS 2024. Lecture Notes in Computer Science(), vol 14840. Springer, Cham. https://doi.org/10.1007/978-3-031-65668-2_1

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  • DOI: https://doi.org/10.1007/978-3-031-65668-2_1

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  • Online ISBN: 978-3-031-65668-2

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