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Multi-granulation-based knowledge discovery in incomplete generalized multi-scale decision systems

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Abstract

Multi-granulation rough sets and multi-scale data analysis are two active topics in granular computing. This study aims to investigate knowledge discovery in incomplete generalized multi-scale decision systems based on multi-granulation rough sets. Multi-granulation structures in incomplete generalized multi-scale decision systems are first discussed and updating mechanisms of information granules with the scale coarsening and refinement are described. Concepts of pessimistic upper and lower optimal scale combinations based on pessimistic multi-granulation rough sets are then defined and their uniqueness is verified. Evidence-theory-based numerical algorithms for finding optimal scale combinations are further designed. Notions of optimistic upper and lower optimal scale combinations based on optimistic multi-granulation rough sets are also introduced and their properties are examined. Finally, reducts of scale combinations are explored and an illustrative example is employed to elaborate multi-granulation rule acquisition approach in incomplete generalized multi-scale decision systems.

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References

  1. Bao H, Wu WZ, Zheng JW, Li TJ (2021) Entropy based optimal scale combination selection for generalized multi-scale information tables. Int J Mach Learn Cybern 12:1427–1437

    Google Scholar 

  2. Bargiela A, Pedrycz W (2008) Toward a theory of granular computing for human-centred information processing. IEEE Trans Fuzzy Syst 16(2):320–330

    Google Scholar 

  3. Che XY, Mi JS, Chen DG (2018) Information fusion and numerical characterization of a multi-source information system. Knowl-Based Syst 145:121–133

    Google Scholar 

  4. Chen YS, Li JH, Li JJ, Lin RD, Chen DX (2022) A further study on optimal scale selection in dynamic multi-scale decision information systems based on sequential three-way decisions. Int J Mach Learn Cybern 13:1505–1515

    Google Scholar 

  5. Chen CLP, Zhang CY (2014) Data-intensive applications, challenges, techniques and technologies: a survey on big data. Inf Sci 275:314–347

    Google Scholar 

  6. Cheng YL, Zhang QH, Wang GY (2021) Optimal scale combination selection for multi-scale decision tables based on three-way decision. Int J Mach Learn Cybern 12:281–301

    Google Scholar 

  7. Cheng YL, Zhang QH, Wang GY, Hu BQ (2020) Optimal scale selection and attribute reduction in multi-scale decision tables based on three-way decision. Inf Sci 541:36–59

    MathSciNet  Google Scholar 

  8. Hao C, Li JH, Fan M, Liu WQ, Tsang ECC (2017) Optimal scale selection in dynamic multi-scale decision tables based on sequential three-way decisions. Inf Sci 415:213–232

    Google Scholar 

  9. Huang ZH, Li JJ (2021) Multi-scale covering rough sets with applications to data classification. Appl Soft Comput 110:107736

    Google Scholar 

  10. Huang ZH, Li JJ (2022) Feature subset selection with multi-scale fuzzy granulation. IEEE Transact Artif Intell. https://doi.org/10.1109/TAI.2022.3144242

    Article  Google Scholar 

  11. Huang B, Li HX, Feng GF, Guo CX, Chen DF (2021) Double-quantitative rough sets, optimal scale selection and reduction in multi-scale dominance IF decision tables. Int J Approximate Reason 130:170–191

    MathSciNet  MATH  Google Scholar 

  12. Huang B, Li HX, Feng GF, Zhou XZ (2019) Dominance-based rough sets in multi-scale intuitionistic fuzzy decision tables. Appl Math Comput 348:487–512

    MathSciNet  MATH  Google Scholar 

  13. Huang B, Wu WZ, Yan JJ, Li HX, Zhou XZ (2020) Inclusion measure-based multi-granulation decision-theoretic rough sets in multi-scale intuitionistic fuzzy information tables. Inf Sci 507:421–448

    Google Scholar 

  14. Ju HR, Li HX, Yang XB, Zhou XZ, Huang B (2017) Cost-sensitive rough set: a multi-granulation approach. Knowl-Based Syst 123:137–153

    Google Scholar 

  15. Kryszkiewicz M (1998) Rough set approach to incomplete information systems. Inf Sci 112:39–49

    MathSciNet  MATH  Google Scholar 

  16. Leung Y, Fischer MM, Wu WZ, Mi JS (2008) A rough set approach for the discovery of classification rules in interval-valued information systems. Int J Approximate Reason 47(2):233–246

    MathSciNet  MATH  Google Scholar 

  17. Leung Y, Wu WZ, Zhang WX (2006) Knowledge acquisition in incomplete information systems: a rough set approach. Eur J Oper Res 168:164–180

    MathSciNet  MATH  Google Scholar 

  18. Li F, Hu BQ (2017) A new approach of optimal scale selection to multi-scale decision tables. Inf Sci 381:193–208

    Google Scholar 

  19. Li WK, Li JJ, Huang JX, Dai WZ, Zhang XP (2021) A new rough set model based on multi-scale covering. Int J Mach Learn Cybern 12:243–256

    Google Scholar 

  20. Li ZW, Wang ZH, Li QG, Wang P, Wen CF (2021) Uncertainty measurement for a fuzzy set-valued information system. Int J Mach Learn Cybern 12:1769–1787

    Google Scholar 

  21. Li WT, Zhou HX, Xu WH, Wang XZ, Pedrycz W (2022) Interval dominance-based feature selection for interval-valued ordered data. IEEE Transact Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3184120

    Article  Google Scholar 

  22. Liang JY, Qian YH, Li DY, Hu QH (2015) Theory and method of granular computing for big data mining (in Chinese). Scientia Sinica Inform 45(11):1355–1369

    Google Scholar 

  23. Luo C, Li TR, Chen HM, Fujita H, Yi Z (2018) Incremental rough set approach for hierarchical multicriteria classification. Inf Sci 429:72–87

    MathSciNet  MATH  Google Scholar 

  24. Pang JF, Guan XQ, Liang JY, Wang BL, Song P (2020) Multi-attribute group decision-making method based on multi-granulation weights and three-way decisions. Int J Approximate Reason 117:122–147

    MathSciNet  MATH  Google Scholar 

  25. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston

    MATH  Google Scholar 

  26. Pedrycz W, Skowron A, Kreinovich V (2008) Handbook of granular computing. Wiley, New York

    Google Scholar 

  27. Qian YH, Dang CY, Liang JY, Tang DW (2009) Set-valued ordered information systems. Inf Sci 179(16):2809–2832

    MathSciNet  MATH  Google Scholar 

  28. Qian YH, Li SY, Liang JY, Shi ZZ, Wang F (2014) Pessimistic rough set based decisions: a multigranulation fusion strategy. Inf Sci 264:196–210

    MathSciNet  MATH  Google Scholar 

  29. Qian YH, Liang JY, Dang CY (2010) Incomplete multigranulation rough set. IEEE Transact Syst Man Cybern-Part A 40(2):420–431

    Google Scholar 

  30. Qian YH, Liang JY, Yao YY, Dang CY (2010) MGRS: a multi-granulation rough set. Inf Sci 180(6):949–970

    MathSciNet  MATH  Google Scholar 

  31. Qian J, Liu CH, Miao DQ, Yue XD (2020) Sequential three-way decisions via multi-granularity. Inf Sci 507:606–629

    MathSciNet  MATH  Google Scholar 

  32. Qian J, Liu CH, Yue XD (2019) Multigranulation sequential three-way decisions based on multiple thresholds. Int J Approximate Reason 105:396–416

    MathSciNet  MATH  Google Scholar 

  33. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton

    MATH  Google Scholar 

  34. She YH, Qian ZH, He XL, Wang JT, Qian T, Zheng WL (2021) On generalization reducts in multi-scale decision tables. Inf Sci 555:104–124

    MathSciNet  MATH  Google Scholar 

  35. Tan AH, Wu WZ, Li JJ, Lin GP (2016) Evidence-theory-based numerical characterization of multigranulation rough sets in incomplete information systems. Fuzzy Sets Syst 294:18–35

    MathSciNet  MATH  Google Scholar 

  36. Tan AH, Wu WZ, Li JJ, Li TJ (2020) Reduction foundation with multigranulation rough sets using discernibility. Artif Intell Rev 53:2425–2452

    Google Scholar 

  37. Tan AH, Wu WZ, Tao YZ (2017) On the belief structures and reductions of multigranulation spaces with decisions. Int J Approximate Reason 88:39–52

    MathSciNet  MATH  Google Scholar 

  38. Wang HR, Li WT, Zhan T, Yuan KH, Xu XC (2021) Multi-granulation-based optimal scale selection in multi-scale information systems. Comput Electr Eng 92:107107

    Google Scholar 

  39. Wang Y, Sun BZ, Zhang XR, Wang Q (2020) BWM and MULTIMOORA-based multigranulation sequential three-way decision model for multi-attribute group decision-making problem. Int J Approximate Reason 125:169–186

    MathSciNet  MATH  Google Scholar 

  40. Wu WZ (2008) Attribute reduction based on evidence theory in incomplete decision systems. Inf Sci 178(5):1355–1371

    MathSciNet  MATH  Google Scholar 

  41. Wu WZ, Leung Y (2011) Theory and applications of granular labelled partitions in multi-scale decision tables. Inf Sci 181(18):3878–3897

    MATH  Google Scholar 

  42. Wu WZ, Leung Y (2013) Optimal scale selection for multi-scale decision tables. Int J Approximate Reason 54(8):1107–1129

    MathSciNet  MATH  Google Scholar 

  43. Wu WZ, Leung Y (2020) A comparison study of optimal scale combination selection in generalized multi-scale decision tables. Int J Mach Learn Cybern 11:961–972

    Google Scholar 

  44. Wu WZ, Qian YH, Li TJ, Gu SM (2017) On rule acquisition in incomplete multi-scale decision tables. Inf Sci 378:282–302

    MathSciNet  MATH  Google Scholar 

  45. Wu WZ, Yang L, Tan AH, Xu YH (2018) Granularity selections in generalized incomplete multi-granular labeled decision systems (in Chinese). J Comput Res Develop 55(6):1263–1272

    Google Scholar 

  46. Xu WH, Li WT (2016) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Transact Cybern 46(2):366–379

    MathSciNet  Google Scholar 

  47. Xu WH, Yuan KH, Li WT, Ding WP (2022) An emerging fuzzy feature selection method using composite entropy-based uncertainty measure and data distribution. IEEE Transact Emerging Topics Comput Intell. https://doi.org/10.1109/TETCI.2022.3171784

    Article  Google Scholar 

  48. Yang XB, Qi YS, Song XN, Yang JY (2013) Test cost sensitive multigranulation rough set: model and minimal cost selection. Inf Sci 250:184–199

    MathSciNet  MATH  Google Scholar 

  49. Yang L, Xu WH, Zhang XY, Sang BB (2020) Multi-granulation method for information fusion in multi-source decision information system. Int J Approximate Reason 122:47–65

    MathSciNet  MATH  Google Scholar 

  50. Yang XB, Zhang YQ, Yang JY (2012) Local and global measurements of MGRS rules. Int J Comput Intell Syst 5(6):1010–1024

    MathSciNet  Google Scholar 

  51. Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90(2):111–127

    MathSciNet  MATH  Google Scholar 

  52. Zhang QH, Cheng YL, Zhao F, Wang GY, Xia SY (2022) Optimal scale combination selection integrating three-way decision with hasse diagram. IEEE Transact Neural Netw Learn Syst 33(8):3675–3689

    MathSciNet  Google Scholar 

  53. Zhang CL, Li JJ, Lin YD (2021) Knowledge reduction of pessimistic multigranulation rough sets in incomplete information systems. Soft Comput 25:12825–12838

    Google Scholar 

  54. Zhang PF, Li TR, Luo C, Wang GQ (2022) AMG-DTRS: adaptive multi-granulation decision-theoretic rough sets. Int J Approximate Reason 140:7–30

    MathSciNet  MATH  Google Scholar 

  55. Zhang XQ, Zhang QH, Cheng YL, Wang GY (2020) Optimal scale selection by integrating uncertainty and cost-sensitive learning in multi-scale decision tables. Int J Mach Learn Cybern 11:1095–1114

    Google Scholar 

  56. Zheng JW, Wu WZ, Bao H, Tan AH (2022) Evidence theory based optimal scale selection for multi-scale ordered decision systems. Int J Mach Learn Cybern 13:1115–1129

    Google Scholar 

  57. Zhu YJ, Yang B (2022) Optimal scale combination selection for inconsistent multi-scale decision tables. Soft Comput 26:6119–6129

    Google Scholar 

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Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (grant numbers 61976194 and 62076221).

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Authors and Affiliations

  1. School of Information Engineering, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Jinbo Wang, Wei-Zhi Wu & Anhui Tan

  2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Jinbo Wang, Wei-Zhi Wu & Anhui Tan

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  1. Jinbo Wang
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Correspondence to Wei-Zhi Wu.

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Wang, J., Wu, WZ. & Tan, A. Multi-granulation-based knowledge discovery in incomplete generalized multi-scale decision systems. Int. J. Mach. Learn. & Cyber. 13, 3963–3979 (2022). https://doi.org/10.1007/s13042-022-01634-3

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