Skip to main content
SpringerLink
Log in

A comparison study of optimal scale combination selection in generalized multi-scale decision tables

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Traditional rough set approach is mainly used to unravel rules from a decision table in which objects can possess a unique attribute-value. In a real world data set, for the same attribute objects are usually measured at different scales. The main objective of this paper is to study optimal scale combinations in generalized multi-scale decision tables. A generalized multi-scale information table is an attribute-value system in which different attributes are measured at different levels of scales. With the aim of investigating knowledge representation and knowledge acquisition in inconsistent generalized multi-scale decision tables, we first introduce the notion of scale combinations in a generalized multi-scale information table. We then formulate information granules with different scale combinations in multi-scale information systems and discuss their relationships. Furthermore, we define lower and upper approximations of sets with different scale combinations and examine their properties. Finally, we examine optimal scale combinations in inconsistent generalized multi-scale decision tables. We clarify relationships among different concepts of optimal scale combinations in inconsistent generalized multi-scale decision tables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Bargiela A, Pedrycz W (2002) Granular computing: an introduction. Kluwer Academic Publishers, Boston

    MATH  Google Scholar 

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

    Google Scholar 

  3. Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relation. Int J Intell Syst 17:153–171

    MATH  Google Scholar 

  4. Grzymala-Busse JW, Zuo X (1998) Classification strategies using certain and possible rules. In: Polkowski L, Skowron A(Eds.), Rough Sets and Current Trends in Computing. Lecture Notes in Computer Science 1424: 37–44

  5. Gu SM, Wu WZ (2013) On knowledge acquisition in multi-scale decision systems. Int J Mach Learn Cyb 4:477–486

    Google Scholar 

  6. 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 

  7. Hong TP, Tseng LH, Wang SL (2002) Learning rules from incomplete training examples by rough sets. Expert Syst Appl 22:285–293

    Google Scholar 

  8. Inuiguchi M, Hirano S, Tsumoto S (2002) Rough set theory and granular computing. Springer, Berlin

    MATH  Google Scholar 

  9. Komorowski J, Pawlak Z, Polkowski L, Skowron A (1999) Rough sets: tutorial. In: Pal SK, Skowron A (eds) Rough fuzzy hybridization, a new trend in decision making. Springer, Berlin, pp 3–98

    Google Scholar 

  10. Leung Y, Li DY (2003) Maximal consistent block technique for rule acquisition in incomplete information systems. Inf Sci 153:85–106

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  12. Leung Y, Zhang JS, Xu ZB (2000) Clustering by scale-space filtering. IEEE Trans Pattern Anal Mach Intell 22:1396–1410

    Google Scholar 

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

    Google Scholar 

  14. Li F, Hu BQ, Wang J (2017) Stepwise optimal scale selection for multi-scale decision tables via attribute significance. Knowl Based Syst 129:4–16

    Google Scholar 

  15. Li JH, Ren Y, Mei CL, Qian YH, Yang XB (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowl Based Syst 91:152–164

    Google Scholar 

  16. Lin TY (1997) Granular computing: From rough sets and neighborhood systems to information granulation and computing with words. In: European congress on intelligent techniques and soft computing, September 8-12: 1602–1606

  17. Lin TY, Yao YY, Zadeh LA (2002) Data mining, rough sets and granular computing. Physica-Verlag, Heidelberg

    MATH  Google Scholar 

  18. Lingras PJ, Yao YY (1998) Data mining using extensions of the rough set model. J Am Soc Inf Sci 49:415–422

    Google Scholar 

  19. 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  Google Scholar 

  20. Luo C, Li TR, Huang YY, Fujita H (2019) Updating three-way decisions in incomplete multi-scale information systems. Inf Sci 476:274–289

    Google Scholar 

  21. Ma JM, Zhang WX, Leung Y, Song XX (2007) Granular computing and dual Galois connection. Inf Sci 177:5365–5377

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  23. Pawlak Z (2001) Drawing conclusions from data–the rough set way. Int J Intell Syst 16:3–11

    MATH  Google Scholar 

  24. Pedrycz W (2001) Granular computing: an emerging paradigm. Physica-Verlag, Heidelberg

    MATH  Google Scholar 

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

    Google Scholar 

  26. Polkowski L, Tsumoto S, Lin TY (2000) Rough set methods and applications. Physica-Verlag, Berlin

    Google Scholar 

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

    MATH  Google Scholar 

  28. She YH, Li JH, Yang HL (2015) A local approach to rule induction in multi-scale decision tables. Knowl Based Syst 89:398–410

    Google Scholar 

  29. Skowron A (1989) The relationship between rough set theory and evidence theory. Bull Pol Acad Sci 37:87–90

    Google Scholar 

  30. Skowron A (1990) The rough sets theory and evidence theory. Fund Inf 13:245–262

    MathSciNet  MATH  Google Scholar 

  31. Skowron A, Grzymala-Busse J (1994) From rough set theory to evidence theory. In: Yager RR, Fedrizzi M, Kacprzyk J (eds) Advance in the Dempster-Shafer theory of evidence. Wiley, New York, pp 193–236

    Google Scholar 

  32. Skowron A, Stepaniuk J (2001) Information granules: towards foundations of granular computing. Int J Intell Syst 16:57–85

    MATH  Google Scholar 

  33. Skowron A, Stepaniuk J, Swiniarski RW (2012) Modeling rough granular computing based on approximation spaces. Inf Sci 184:20–43

    MATH  Google Scholar 

  34. Wu WZ, Chen CJ, Li TJ, Xu YH (2016) Comparative study on optimal granularities in inconsistent multi-granular labeled decision systems. Pat Recogn Artif Intell 29(12):1103–1111

    Google Scholar 

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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  37. Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21:1461–1474

    Google Scholar 

  38. Wu WZ, Leung Y, Zhang WX (2002) Connections between rough set theory and Dempster-Shafer theory of evidence. Int J General Syst 31:405–430

    MathSciNet  MATH  Google Scholar 

  39. 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 

  40. Wu WZ, Zhang M, Li HZ, Mi JS (2005) Knowledge reduction in random information systems via Dempster-Shafer theory of evidence. Inf Sci 174:143–164

    MathSciNet  MATH  Google Scholar 

  41. Xie JP, Yang MH, Li JH, Zheng Z (2018) Rule acquisition and optimal scale selection in multi-scale formal decision contexts and their applications to smart city. Future Gener Comput Syst 83:564–581

    Google Scholar 

  42. Xu YH, Wu WZ, Tan AH (2017) Optimal scale selections in consistent generalized multi-scale decision tables. In: Proceedings of international joint conference on rough sets, July 3-7, 2017, Olsztyn, Poland. Lecture Notes in Artificial Intelligence. Springer, Berlin, 10313: 185–198

  43. Yager RR (2008) Intelligent social network analysis using granular computing. Int J Intell Syst 23:1196–1219

    MATH  Google Scholar 

  44. Yao JT (2008) Recent developments in granular computing: A bibliometrics study. In: Proceedings of IEEE International Conference on Granular Computing, Hangzhou, China, Aug 26–28, 2008: 74–79

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

    MATH  Google Scholar 

  46. Yao YY (2004) A partition model of granular computing, transactions on rough sets I. Lect Notes Comput Sci 3100:232–253

    Google Scholar 

  47. Yao YY, Liau CJ, Zhong N (2003) Granular computing based on rough sets, quotient space theory, and belief functions. In: Proceedings of the 14th international symposium on foundations of intelligent systems. Lecture Notes in Computer Science, Springer, Berlin, 2871: 152–159

  48. Yao YY, Lingras PJ (1998) Interpretations of belief functions in the theory of rough sets. Inf Sci 104:81–106

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  50. Zhang YQ (2005) Constructive granular systems with universal approximation and fast knowledge discovery. IEEE Trans Fuzzy Syst 13:48–57

    Google Scholar 

  51. Zhang WX, Leung Y, Wu WZ (2003) Information systems and knowledge discovery (in Chinese). Science Press, Beijing

    Google Scholar 

Download references

Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (Grant numbers 41631179 and 61573321) and the Zhejiang Provincial Natural Science Foundation of China (Grant number LY18F030017).

Author information

Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Wei-Zhi Wu

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

    Wei-Zhi Wu

  3. Institute of Future Cities and Stanley Ho Big Data Decision Analytics Research Centre, The Chinese University of Hong Kong, Hong Kong, People’s Republic of China

    Yee Leung

  4. Department of Geography and Resource Management, The Chinese University of Hong Kong, Hong Kong, People’s Republic of China

    Yee Leung

Authors
  1. Wei-Zhi Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yee Leung
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei-Zhi Wu.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, WZ., Leung, Y. A comparison study of optimal scale combination selection in generalized multi-scale decision tables. Int. J. Mach. Learn. & Cyber. 11, 961–972 (2020). https://doi.org/10.1007/s13042-019-00954-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-019-00954-1

Keywords

Search

Navigation