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Constructing Three-Way Decision of Rough Fuzzy Sets from the Perspective of Uncertainties

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Abstract

From the perspective of human cognition, three-way decision (3WD) explores thinking, problem solving, and information processing in three paradigms. Rough fuzzy sets (RFS) are constructed to handle fuzzy concepts by extending the classical rough sets. In three-way decision with rough fuzzy sets (3WDRFS), current works are mainly concerned with calculating the thresholds according to the given risk parameters to make 3WD with minimum cost. However, in real applications, the risk parameters are given in a subjective way based on expert experience. As a result, the risk parameters may be difficult to accurately obtain in 3WDRFS. To solve this problem, uncertainty measure is introduced into 3WDRFS, which provides a new perspective for 3WD theory. First, the fuzziness-based uncertainty for the average-step-fuzzy sets of RFS is analyzed. Then, based on the average-step-fuzzy sets, a 3WDRFS is proposed with the idea of minimizing the uncertainty loss. Furthermore, the sequential three-way decision of RFS (S3WDRFS) with adaptive thresholds from the perspective of fuzziness is presented. The relevant experiments suggest that the objective function designed in the proposed 3WDRFS is effective and reasonable. Moreover, 3WDRFS based on uncertainty loss has better performance than 0.5-approximation model.

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Data Availability

The datasets generated during and/or analyzed during the current study are available in the UCI repository, https://archive.ics.uci.edu/ml/datasets.php.

References

  1. Zadeh LA. Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 1997;90(2):111–27.

    MathSciNet  Google Scholar 

  2. Pedrycz W, Bargiela A. An optimization of allocation of information granularity in the interpretation of data structures. IEEE Trans Syst Man Cybern. 2012;42(3):582–90.

    Google Scholar 

  3. Wang GY, Yang J, Xu J. Granular computing: from granularity optimization to multi-granularity joint problem solving. Granular Computing. 2017;2(3):582–90.

    Google Scholar 

  4. Zadeh LA. Fuzzy sets. Inf Control. 1965;8(3):338–53.

    Google Scholar 

  5. Zhang L, Zhang B. The quotient space theory of problem solving. Fund Inform. 2004;59(2–3):287–98.

    MathSciNet  Google Scholar 

  6. Pawlak Z. Rough sets. International Journal of Computer & Information Sciences. 1982;11(5):341–56.

    MathSciNet  Google Scholar 

  7. Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst. 1990;109(2–3):191–209.

    Google Scholar 

  8. Sun BZ, Ma WM, Chen XT. Variable precision multigranulation rough fuzzy set approach to multiple attribute group decision-making based on \(\lambda\)-similarity relation. Comput Ind Eng. 2019;127:326–343.

  9. Chen XW, Xu WH. Double-quantitative multigranulation rough fuzzy set based on logical operations in multi-source decision systems. Int J Mach Learn Cybern. 2022;13(4):1021–48.

    Google Scholar 

  10. Zhang QH, Wang J, Wang GY. The approximate representation of rough-fuzzy sets. Chin J Comput. 2015;38(7):1484–96.

    MathSciNet  Google Scholar 

  11. Zhang QH, Wang J, Wang GY, Yu H. The approximation set of a vague set in rough approximation space. Inform Sci. 2015;300:1–19.

    MathSciNet  Google Scholar 

  12. Zhang QH, Yang JJ, Yao LY. Attribute reduction based on rough approximation set in algebra and information views. IEEE Access. 2016;4:5399–407.

    Google Scholar 

  13. Yao LY, Zhang QH, Hu SP, Zhang Q. Rough entropy for image segmentation based on approximation sets and particle swarm optimization. J Front Comput Sc Technol. 2016;10(5):699–708.

    Google Scholar 

  14. Zhang QH, Liu KX. Approximation sets of rough sets and granularity optimization algorithm based on cost-sensitive. J Control Decis. 2020;35(9):2070–80.

    Google Scholar 

  15. Yao YY. Tri-level thinking: models of three-way decision. Int J Mach Learn Cybern. 2020;11(5):947–59.

    Google Scholar 

  16. Yang JL, Yao YY. A three-way decision based construction of shadowed sets from atanassov intuitionistic fuzzy sets. Inform Sci. 2021;577:1–21.

    MathSciNet  Google Scholar 

  17. Yao YY. Three-way granular computing, rough sets, and formal concept analysis. Int J Approx Reason. 2020;116:106–25.

    MathSciNet  Google Scholar 

  18. Yao YY. The geometry of three-way decision. Appl Intell. 2021;51(9):6298–325.

    Google Scholar 

  19. Yao YY. Symbols-meaning-value (smv) space as a basis for a conceptual model of data science. Int J Approx Reason. 2022;144:113–28.

    MathSciNet  Google Scholar 

  20. Ju HR, Pedrycz W, Li HX, Ding WP, Yang XB, Zhou XZ. Sequential three-way classifier with justifiable granularity. Knowl-Based Syst. 2019;163:103–19.

    Google Scholar 

  21. Zhi HL, Li JH. Granule description of incomplete data: a cognitive viewpoint. Cogn Comput. 2021;2:1–12.

    Google Scholar 

  22. Lang GM, Luo JF, Yao YY. Three-way conflict analysis: a unification of models based on rough sets and formal concept analysis. Knowl-Based Syst. 2020;194(22).

    Google Scholar 

  23. Yao YY. A triarchic theory of granular computing. Granular Computing. 2016;1(2):145–57.

    Google Scholar 

  24. Li WW, Jia XY, Wang L, Zhou B. Multi-objective attribute reduction in three-way decision-theoretic rough set model. Int J Approx Reason. 2019;105:327–41.

    MathSciNet  Google Scholar 

  25. Ye XQ, Liu D. An interpretable sequential three-way recommendation based on collaborative topic regression. Expert Syst Appl. 2021;168.

    Google Scholar 

  26. Du JL, Liu SF, Liu Y. A novel grey multi-criteria three-way decisions model and its application. Comput Ind Eng. 2021;158.

    Google Scholar 

  27. Savchenko AV. Sequential three-way decisions in multi-category image recognition with deep features based on distance factor. Inform Sci. 2019;489:18–36.

    MathSciNet  Google Scholar 

  28. Li HX, Zhang LB, Huang B, Zhou XZ. Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl-Based Syst. 2016;91:241–51.

    Google Scholar 

  29. Afridi MK, Azam N, Yao JT, Alanazi E. A three-way clustering approach for handling missing data using gtrs. Int J Approx Reason. 2018;98:11–24.

    MathSciNet  Google Scholar 

  30. Wang PX, Yao YY. Ce3: A three-way clustering method based on mathematical morphology. Knowl-Based Syst. 2018;155:54–65.

    Google Scholar 

  31. Yao JT, Azam N. Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets. IEEE Trans Fuzzy Syst. 2015;23(1):3–15.

    Google Scholar 

  32. Li ZW, Zhang PF, Xie NX, Zhang GQ, Wen CF. A novel three-way decision method in a hybrid information system with images and its application in medical diagnosis. Eng Appl Artif Intell. 2020;92.

    Google Scholar 

  33. Wang JJ, Ma XL, Xu ZH, Zhan JM. Regret theory-based three-way decision model in hesitant fuzzy environments and its application to medical decision. IEEE Trans Fuzzy Syst. 2022;1.

  34. He SF, Wang YM, Pan XH, Chin KS. A novel behavioral three-way decision model with application to the treatment of mild symptoms of covid-19. Appl Soft Comput. 2022;124.

    Google Scholar 

  35. Yao YY, Deng XF. Sequential three-way decisions with probabilistic rough sets. In: IEEE International Conference on Cognitive Informatics and Cognitive Computing. 2011;pp. 120–125

  36. Sun BZ, Ma WM, Zhao HY. Decision-theoretic rough fuzzy set model and application. Inform Sci. 2014;283:180–96.

    MathSciNet  Google Scholar 

  37. Sun BZ, Ma WM, Li BJ, Li XN. Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set. Int J Approx Reason. 2018;93:424–42.

    MathSciNet  Google Scholar 

  38. Ma JM, Zhang HY, Qian YH. Three-way decisions with reflexive probabilistic rough fuzzy sets. Granular Computing. 2019;4(3):363–75.

    Google Scholar 

  39. Yang J, Wang GY, Zhang QH, Chen YH, Xu TH. Optimal granularity selection based on cost-sensitive sequential three-way decisions with rough fuzzy sets. Knowl-Based Syst. 2019;163:131–44.

    Google Scholar 

  40. Zhai JH, Zhang Y, Zhu HY. Three-way decisions model based on tolerance rough fuzzy set. Int J Mach Learn Cybern. 2017;8(1):35–43.

    Google Scholar 

  41. Zhang XY, Yao YY. Tri-level attribute reduction in rough set theory. Expert Syst Appl. 2022;190.

    Google Scholar 

  42. Yu H, Chen LY, Yao JT. A three-way density peak clustering method based on evidence theory. Knowl-Based Syst. 2021;211.

    Google Scholar 

  43. Deng J, Zhan JM, Xu ZS, Herrera-Viedma E. Regret-theoretic multi-attribute decision-making model using three-way framework in multi-scale information systems. IEEE Trans Cybern. 2022;1–14.

  44. Deng J, Zhan JM, Herrera-Viedma EFH. Regret theory-based three-way decision method on incomplete multi-scale decision information systems with interval fuzzy numbers. IEEE Trans Fuzzy Syst. 2022;1-15.

  45. Wang WJ, Zhan JM, 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. Information Fusion. 2023;89:382–96.

    Google Scholar 

  46. Wang WJ, Zhan JM, Herrera-Viedma E. A three-way decision approach with a probability dominance relation based on prospect theory for incomplete information systems. Inform Sci. 2022;611:199–224.

    Google Scholar 

  47. Mondal A, Roy SK, Pamucar D. Regret-based three-way decision making with possibility dominance and spa theory in incomplete information system. Expert Syst Appl. 2023;211.

    Google Scholar 

  48. Siminski K. 3wdnfs-three-way decision neuro-fuzzy system for classification. Fuzzy Sets Syst. 2022.

  49. Chen J, Chen Y, He YC, Xu Y, Zhao S, Zhang YP. A classified feature representation three-way decision model for sentiment analysis. Appl Intell. 2022;52:7995–8007.

    Google Scholar 

  50. Yao YY, Wang S, Deng XF. Constructing shadowed sets and three-way approximations of fuzzy sets. Inform Sci. 2017;412(5):132–53.

    MathSciNet  Google Scholar 

  51. Zhang QH, Xiao Y, Wang GY. A new method for measuring fuzziness of vague set (or intuitionistic fuzzy set). J Intell Fuzzy Syst. 2013;25(2):505–15.

    MathSciNet  Google Scholar 

  52. Zhang QH, Zhang P, Wang GY. Research on approximation set of rough set based on fuzzy similarity. J Intell Fuzzy Syst. 2017;32(3):2549–62.

    Google Scholar 

  53. Luca AD, Termini S. A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf Control. 1972;20(4):301–12.

    MathSciNet  Google Scholar 

  54. Tahayori H, Sadeghian A, Pedrycz W. Induction of shadowed sets based on the gradual grade of fuzziness. IEEE Trans Fuzzy Syst. 2013;21(5):937–49.

    Google Scholar 

  55. Pedrycz W. Shadowed sets: representing and processing fuzzy sets. IEEE Trans Syst Man Cybern. 1998;28(1):103–9.

    Google Scholar 

  56. Herlocker JL, Konstan JA, Terveen K, Riedl JT. Evaluating collaborative filtering recommender systems. ACM Trans Inf Syst. 2004;22(1):5–53.

    Google Scholar 

  57. Li DY, Meng MJ, Shi XM. Membership clouds and membership cloud generators. Journal of Computer Research and Development. 1995;32:16–21.

    Google Scholar 

Download references

Funding

This study was funded by the National Science Foundation of China (Grant number 62066049, Grant number 62221005, Grant number 61936001), Excellent Young Scientific and Technological Talents Foundation of Guizhou Province (QKH-platform talent (2021) Grant number 5627), The Natural Science Foundation of Chongqing (cstc2019jcyj-cxttX0002, cstc2021ycjh-bgzxm0013), The Key Cooperation Project of Chongqing Municipal Education Commission (HZ2021008), and Science and Technology Top Talent Project of Guizhou Education Department (QJJ2022[088]).

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Authors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Jie Yang, Xiaoqi Wang, Guoyin Wang & Deyou Xia

  2. School of Physics and Electronic Science, Zunyi Normal University, Zunyi, 563002, China

    Jie Yang

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  1. Jie Yang
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Correspondence to Jie Yang.

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Yang, J., Wang, X., Wang, G. et al. Constructing Three-Way Decision of Rough Fuzzy Sets from the Perspective of Uncertainties. Cogn Comput 16, 2454–2470 (2024). https://doi.org/10.1007/s12559-023-10147-2

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