Skip to main content
SpringerLink
Log in

Double-quantitative multigranulation decision-theoretic rough fuzzy set model

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

Abstract

Probabilistic rough set model and graded rough set model are used to measure relative quantitative information and absolute quantitative information between equivalence classes and basic concepts, respectively. Since fuzzy concepts are more common in real life than classical concepts, how to use relative and absolute quantitative information to determine fuzzy concepts is a extremely important research topic. In this study, we propose a double-quantitative decision theory rough fuzzy set frame based on the fusion of decision theory rough set and graded rough set, and the framework mainly studies the fuzzy concepts in multigranulation approximation spaces. Three pairs of double-quantitative multigranulation decision theory rough fuzzy set models are established. Some basic characteristics of these models are discussed. The decision rules including relative and absolute quantitative information are studied. The intrinsic relationship between the double-quantitative decision theory rough fuzzy set and the multigranulation rough set is analyzed. Finally, an illustrative case of medical diagnosis is conducted to explain and evaluate the dual quantitative decision theory approach.

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

Similar content being viewed by others

References

  1. Pawlak Z (1982) Rough set. Int J Comput Inf Sci 11(5):341–356

    MATH  Google Scholar 

  2. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic, Dordrecht

    MATH  Google Scholar 

  3. Zhao XR, Hu BQ (2016) Fuzzy probabilistic rough sets and their corresponding three-way decisions. Knowl Based Syst 91:126–142

    Google Scholar 

  4. Zhang XH, Miao DQ, Liu CH, Le ML (2016) Constructive methods of rough approximation operators and multigranulation rough sets. Knowl Based Syst 91:114–125

    Google Scholar 

  5. Zhang YL, Li CQ, Lin ML, Lin YJ (2015) Relationships between generalized rough sets based on covering and reflexive neighborhood system. Inf Sci 319:56–67

    MathSciNet  MATH  Google Scholar 

  6. Yao YY, Zhou B (2016) Two bayesian approaches to rough sets. Eur J Oper Res 251(3):904–917

    MathSciNet  MATH  Google Scholar 

  7. Zhang QH, Zhang Q, Wang GY (2016) The uncertainty of probabilistic rough sets in multigranulation spaces. Int J Approx Reason 77:38–54

    MATH  Google Scholar 

  8. Liang JY, Chin KS, Dang C et al (2002) A new method for measuring uncertainty and fuzziness in rough set theory. Int J Gen Syst 31(4):331–342

    MathSciNet  MATH  Google Scholar 

  9. Chen DG, Kwong S, He Q, Wang H (2012) Geometrical interpretation and applications of membership functions with fuzzy rough sets. Fuzzy Sets Syst 193:122–135

    MathSciNet  MATH  Google Scholar 

  10. Tan AH, Li JJ, Lin GP (2015) Extended results on the relationship between information systems. Inf Sci 290:156–173

    MathSciNet  MATH  Google Scholar 

  11. Liang JY, Wang JH, Qian YH (2014) A new measure of uncertainty based on knowledge granulation for rough sets. Inf Sci 26(2):294–308

    Google Scholar 

  12. Wu WZ, Zhang M, Li HZ, Mi JS (2005) Knowledge reduction in random information systems via Dempster-Shafer theory of evidence. Inf Sci 174(3):143–164

    MathSciNet  MATH  Google Scholar 

  13. Zhu W (2009) Relationship among basic concepts in covering-based rough sets. Inf Sci 179(14):2478–2486

    MathSciNet  MATH  Google Scholar 

  14. Zhu W, Wang SP (2013) Rough matroids based on relations. Inf Sci 232:241–252

    MathSciNet  MATH  Google Scholar 

  15. 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 

  16. Wang GY, Ma XA, Yu H (2015) Monotonic uncertainty measures for attribute reduction in probabilistic rough set model. Int J Approx Reason 59:41–67

    MathSciNet  MATH  Google Scholar 

  17. Xue Z, Zeng X, Koehl L, Chen Y (2014) Measuring consistency of two datasets using fuzzy techniques and the concept of indiscernibility: application to human perceptions on fabrics. Eng Appl Artif Intell 36:54–63

    Google Scholar 

  18. Chen DG, Li WL, Kwong S (2014) Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets. Int J Approx Reason 55(3):908–923

    MathSciNet  MATH  Google Scholar 

  19. Chen DG, Zhang XX, Li WL (2015) On measurements of covering rough sets based on granules and evidence theory. Inf Sci 317:329–348

    MathSciNet  MATH  Google Scholar 

  20. Pawlak Z, Wong SK, Ziarko W (1988) Rough sets: probabilistic versus deterministic approach. Int J Man Mach Stud 29(1):81–95

    MATH  Google Scholar 

  21. Wong SKM, Ziarko W (1987) INFER: an adaptative decision support system based on the probabilistic approximate classification. International workshop on expert systems and their applications, pp 713–726

  22. Wong SKM, Ziarko W (1987) Comparison of the probabilistic approximate classification and the fuzzy set model. Fuzzy Sets Syst 21(3):357–362

    MathSciNet  MATH  Google Scholar 

  23. Yao YY, Wong SKM, Lingras P (1990) A decision-theoretic rough set model. Methodologies for Intelligent Systems, North-Holland, New York

  24. Pawlak Z, Skowron A (1994) Rough membership functions. Advances in the Dempster–Shafer Theory of Evidence. Wiley, New York, pp 251–271

  25. Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fund Inf 27:245–253

    MathSciNet  MATH  Google Scholar 

  26. Slezak D, Ziarko W (2005) The investigation of the Bayesian rough set model. Int J Approx Reason 40:81–91

    MathSciNet  MATH  Google Scholar 

  27. Herbert JP, Yao JT (2011) Game-theoretic rough set. Fund Inf 108:267–286

    MathSciNet  MATH  Google Scholar 

  28. Yao YY, Zhou B (2010) Naive Bayesian rough sets. In: Proceedings of the 5th international conference on rough sets and knowledge technology, vol 6401. LNAI, pp 713–720

  29. Zhang XY, Miao DQ (2015) An expanded double-quantitative model regarding probabilities and grades and its hierarchical double-quantitative attribute reduction. Inf Sci 299:312–336

    MathSciNet  MATH  Google Scholar 

  30. Zhang XY, Miao DQ (2016) Double-quantitative fusion of accuracy and importance: systematic measure mining, benign integration construction, hierarchical attribute reduction. Knowl Based Syst 91:219–240

    Google Scholar 

  31. Zhang XY, Miao DQ (2013) Two basic double-quantitative rough set models for precision and graded and their investigation using granular computing. Int J Approx Reason 54:1130–1148

    MATH  Google Scholar 

  32. Zhang XY, Miao DQ (2014) Quantitative information architecture, granular computing and rough set models in the double-quantitative approximation space of precision and grade. Inf Sci 268(2):147–168

    MathSciNet  MATH  Google Scholar 

  33. Zadeh LA (1979) Fuzzy sets and information granularity. In: Gupa N, Ragade R, Yager R (eds) Advances in fuzzy set theory and applications. North-Holland, Amsterdam, pp 3–18

  34. Qian YH, Liang JY (2006) Rough set method based on multigranulations, ICCI2006, cognitiveinformatics. IEEE Int. Conf. Cognit. Inf. pp 297-304

  35. Malyszko D, Stepaniuk J (2010) Adaptive multilevel rough entropy evolutionary thresholding. Inf Sci 180(7):1138–1158

    MathSciNet  MATH  Google Scholar 

  36. 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 

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

    MathSciNet  MATH  Google Scholar 

  38. Lin YJ, Li JJ, Lin PR, Lin GP, Chen JK (2014) Feature selection via neighborhood multigranulation fusion. Knowl Based Syst 67:162–168

    Google Scholar 

  39. Qian YH, Liang JY, Dang CY (2010) Incomplete mutigranulation rough set. IEEE Trans Syst Man Cybern Part A 40:420–431

    Google Scholar 

  40. Qian YH, Liang JY, Pedrycz W, Dang CY (2010) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174:597–618

    MathSciNet  MATH  Google Scholar 

  41. Qian YH, Liang JY, Pedrycz W, Dang CY (2011) An efficient accelerator for attribute reduction from incomplete data in rough set framework. Pattern Recogn 44:1658–1670

    MATH  Google Scholar 

  42. Dai JH, Hu H, Wu WZ, Qian YH, Huang DB (2018) Maximal-discernibility-pair-based approach to attribute reduction in fuzzy rough sets. IEEE Trans Fuzzy Syst 26(4):2174–2187

    Google Scholar 

  43. Yang XB, Qi Y, Yu HL, Song XN, Yang JY (2014) Updating multigranulation rough approximations with increasing of granular structures. Knowl Based Syst 64:59–69

    Google Scholar 

  44. Dai JH, Xu Q (2013) Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification. Appl Soft Comput 13(1):211–221

    Google Scholar 

  45. Qian YH, Zhang H, Sang YL, Liang JY (2014) Multigranulation decision-theoretic rough sets. Int J Approx Reason 55:225–237

    MathSciNet  MATH  Google Scholar 

  46. She YH, He XL (2012) On the structure of the multigranulation rough set model. Knowl Based Syst 36:81–92

    Google Scholar 

  47. Wu MF (2010) Fuzzy rough set model based on multi-granulations. Int Conf Comput Eng Technol 2010:271–275

    Google Scholar 

  48. Yang XB, Song XN, Dou HL (2011) Multi-granulation rough set: from crisp to fuzzy case. Ann Fuzzy Math Inf 1(1):55–70

    MathSciNet  MATH  Google Scholar 

  49. Xu WH, Wang QR, Zhang XT (2011) Multi-granulation fuzzy rough set models on tolerance relations. In: Proceeding of The Fourth International Workshop on Advanced Computational Intelligence. Wuhan, Hubei, pp 359–366

  50. Liu CH, Wang MZ (2011) Covering fuzzy rough set based on multigranulations. In: Proceedings of International Conference on Uncertainty Reasoning and Knowledge Engineering, pp 146–149

  51. Liu CH, Miao DQ (2011) Covering rough set model based on multi-granulations, RSFD-GRc2011 87-90

    Google Scholar 

  52. Liang JY, Wang F, Dang CY, Qian YH (2012) An efficient rough feature selection algorithm with a multi-granulation view. Int J Approx Reason 53(6):912–926

    MathSciNet  Google Scholar 

  53. Zadeh LA (1965) Fuzzy sets. Inf. Control 8(3):338–353

    MathSciNet  MATH  Google Scholar 

  54. Sarkar M (2002) Rough-fuzzy functions in classification. Fuzzy Sets Syst 132(3):353–369

    MathSciNet  MATH  Google Scholar 

  55. Yao YY, Lin TY (1996) Generalization of rough sets using modal logic. Intell. Autom. Soft Comput. 2(2):103–119

    Google Scholar 

  56. Yao YY, Wong SKM (1992) A decision theoretic framework for approximating concepts. Int J Man Mach Stud 37(6):793–809

    Google Scholar 

  57. Sun BZ, Ma WM, Zhao HY (2014) Decision-theoretic rough fuzzy set model and application. Inf Sci 283:180–196

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11771111) and the National Natural Science Foundation of CQ CSTC (No. CSTC 2015jcyjA40053).

Author information

Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Mengmeng Li & Minghao Chen

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Minghao Chen

  3. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Weihua Xu

Authors
  1. Mengmeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Minghao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Weihua Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minghao Chen.

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

Li, M., Chen, M. & Xu, W. Double-quantitative multigranulation decision-theoretic rough fuzzy set model. Int. J. Mach. Learn. & Cyber. 10, 3225–3244 (2019). https://doi.org/10.1007/s13042-019-01013-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-019-01013-5

Keywords

Search

Navigation