Advertisement

Soft Computing

, Volume 22, Issue 24, pp 8207–8226 | Cite as

Multi-granulation bipolar-valued fuzzy probabilistic rough sets and their corresponding three-way decisions over two universes

  • Prasenjit Mandal
  • A. S. Ranadive
Methodologies and Application

Abstract

This article introduces general framework of multi-granulation bipolar-valued fuzzy (BVF) probabilistic rough sets (MG-BVF-PRSs) models in multi-granulation BVF probabilistic approximation space over two universes. Four types of MG-BVF-PRSs are established, by the four different conditional probabilities of BVF event. For different constraints on parameters, we obtain four kinds of each type MG-BVF-PRSs over two universes. To find a suitable way of explaining and determining these parameters in each kind of each type MG-BVF-PRS, three-way decisions (3WDs) are studied based on Bayesian minimum-risk procedure, i.e., the multi-granulation BVF decision-theoretic rough set (MG-BVF-DTRS) approach. The main contribution of this paper is twofold. One is to extend the fuzzy probabilistic rough set (FPRS) to MG-BVF-PRS model over two universes. Another is to present an approach to select parameters in MG-BVF-PRS modeling by using the process of decision making under conditions of risk.

Keywords

Rough set Fuzzy event Bipolar-valued fuzzy event Multi-granulation bipolar-valued fuzzy probabilistic rough set Three-way decisions 

Notes

Acknowledgements

The authors would like to thank the Associate Editor and reviewers for their thoughtful comments and valuable suggestions. Some tables and figures are directly benefitted from the reviewers comments.

Compliance with ethical standards

Conflict of interest

Prasenjit Mandal and A. S. Ranadive declare that there is no conflict of interest.

Ethical approval

This article does not contain any study performed on humans or animals by the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefGoogle Scholar
  2. Cacioppo JT, Gardner WL, Berntson GG (1997) Beyond bipolar conceptualizations and measures: the case of attitudes and evaluation space. Pers Soc Psychol Rev 1:3–25CrossRefGoogle Scholar
  3. Chen DG, Zhang L, Zhao SY, Hu QH, Zhu PF (2012) A novel algorithm for finding reducts with fuzzy rough sets. IEEE Trans Fuzzy Syst 20(2):385–389CrossRefGoogle Scholar
  4. Deng X, Yao Y (2014) Decision-theoretic three-way approximations of fuzzy sets. Inf Sci 279:702–715MathSciNetCrossRefGoogle Scholar
  5. Dou HL, Yang XB, Fan JY, Xu SP (2012) The models of variable precision multigranulation rough sets, RSKT 2012. LNCS 7414:465–473Google Scholar
  6. Dubois D, Prade H (2008) An introduction to bipolar representations of information and preference. Int J Intell Syst 23:866–877CrossRefGoogle Scholar
  7. Gau WL, Tan JM (1993) Vague sets. IEEE Trans Syst Man Cybern 23:610–614CrossRefGoogle Scholar
  8. Gut A (2013) Probability—a graduate course, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  9. Han Y, Shi P, Chen S (2015) Bipolar-valued rough fuzzy set and its applications to decision information system. IEEE Trans Fuzzy Syst 33(6):2358–2370CrossRefGoogle Scholar
  10. Li JH, Ren Y, Mei CL, Qian YH, Yang XB (2016) A comparative study of multi-granulation rough sets and concept lattices via rule acquisition. Knowl-Based Syst 91:152–164CrossRefGoogle Scholar
  11. Liang DC, Liu D, Pedrycz W, Hu P (2013) Triangular fuzzy decision-theoretic rough sets. Int J Approx Reason 54:1087–1106CrossRefGoogle Scholar
  12. Lin GP, Qian YH, Li JJ (2012) NMGRS—neighborhood-based multigranulation rough sets. Int J Approx Reason 53(7):1080–1093MathSciNetCrossRefGoogle Scholar
  13. Lin GP, Liang JY, Qian YH (2013) Multigranulation rough sets: from partition to covering. Inf Sci 241:101–118MathSciNetCrossRefGoogle Scholar
  14. Lin YJ, Li JJ, Lin PR, Lin GP, Chen JK (2014) Feature selection via neighborhood multi-granulation fusion. Knowl-Based Syst 67:162–168CrossRefGoogle Scholar
  15. Lin G, Liang J, Qian Y, Li J (2016) A fuzzy multigranulation decision-theoretic approach to multi-source fuzzy information systems. Knowl-Based Syst 91:102–113CrossRefGoogle Scholar
  16. Ma W, Sun B (2012a) On relationship between probabilistic rough set and bayesian risk decision over two universes. Int J Gen Syst 41:225–245MathSciNetCrossRefGoogle Scholar
  17. Ma W, Sun B (2012b) Probabilistic rough set over two universes and rough entropy. Int J Approx Reason 53:608–619MathSciNetCrossRefGoogle Scholar
  18. Pawlak Z (1982) Rough set. Int J Comput Inf Sci 11:341–356CrossRefGoogle Scholar
  19. Pdrycz W (2013) Granular computing: analysis and design of intelligent systems. CRC Press, Francis Taylor, Boca RatonCrossRefGoogle Scholar
  20. Qian YH, Liang JY, Pedrycz W, Dang CY (2010a) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174:597–618MathSciNetCrossRefGoogle Scholar
  21. Qian YH, Liang JY, Yao YY, Dang CY (2010b) MGRS–a multi-granulation rough set. Inf Sci 180:949–970MathSciNetCrossRefGoogle Scholar
  22. Qian YH, Zhang H, Sang YL, Liang JY (2014) Multigranulation decision-theoretic rough sets. Int J Approx Reason 55:225–237MathSciNetCrossRefGoogle Scholar
  23. She YH, He XL (2012) On the structure of the multigranulation rough set model. Knowl-Based Syst 36:81–92CrossRefGoogle Scholar
  24. Sun B, Ma W, Zhao H (2014) Decision-theoretic rough fuzzy set model and application. Inf Sci 283:180–196MathSciNetCrossRefGoogle Scholar
  25. Sun B, Ma W, Chen X (2015) Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision-making. Exp Syst 32:507–521CrossRefGoogle Scholar
  26. Sun B, Ma W, Zhao H (2016) An approach to emergency decision making based on decision-theoretic rough set over two universes. Soft Comput 20(9):3617–3628CrossRefGoogle Scholar
  27. Tree GD, Zadrony S, Bronselaer AJ (2010) Handling bipolarity in elementary queries to possibilistic databases. IEEE Trans Fuzzy Syst 18(3):599–612CrossRefGoogle Scholar
  28. Yang HL, Liao X, Wang S, Wang J (2013) Fuzzy probabilistic rough set model on two universes and its applications. Int J Approx Reason 54:1410–1420MathSciNetCrossRefGoogle Scholar
  29. Yang XB, Qi Y, Yu HL, Song XN, Yang JY (2014) Updating multigranulation rough approximations with increasing of granular structures. Knowl-Based Syst 64:59–69CrossRefGoogle Scholar
  30. Yao YY (2001) Information granulation and rough set approximation. Int J Intell Syst 16:87–104CrossRefGoogle Scholar
  31. Yao YY (2007) Decision-theoretic rough set models. Lect Notes Comput Sci 4481:1–12CrossRefGoogle Scholar
  32. Yao YY (2008) Probabilistic rough set approximations. Int J Approx Reason 49:255–271CrossRefGoogle Scholar
  33. Yao YY (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180:341–353MathSciNetCrossRefGoogle Scholar
  34. Yao YY (2011) The superiority of three-way decisions in probabilistic rough set models. Inf Sci 181:1080–1096MathSciNetCrossRefGoogle Scholar
  35. Yao Y, She Y (2016) Rough set models in multigranulation spaces. Inf Sci 327:40–56MathSciNetCrossRefGoogle Scholar
  36. Yao YY, Wong SKW (1992) A decision theoretic framework for approximating concepts. Int J Man-Mach Stud 37:793–809CrossRefGoogle Scholar
  37. Yao YY, Zhou B (2010) Naive Bayesian rough sets. Lect Notes Comput Sci 6401:719–726CrossRefGoogle Scholar
  38. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–358CrossRefGoogle Scholar
  39. Zadeh LA (1968) Probability measures of fuzzy events. J Math Anal Appl 23:421–427MathSciNetCrossRefGoogle Scholar
  40. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8:199–249MathSciNetCrossRefGoogle Scholar
  41. Zadeh LA (1979) Fuzzy sets and information granularity. In: Gupta N, Ragade R, Yager R (eds) Advances in fuzzy set theory and applications. North-Holland, Amsterdam, pp 3–18Google Scholar
  42. Zhang WR (1994) Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. In: Proceeding of IEEE Conference, pp 305–309Google Scholar
  43. Zhang WR (2011) Yin Yang bipolar relativity: a unifying theory of nature, agents and causality with application in quantum computing, cognitive informatics and life sciences. IGI Global, Hersgey and New YorkCrossRefGoogle Scholar
  44. Zhang WR, Zhang L (2004) Yin Yang bipolar logic and bipolar fuzzy logic. Inf Sci 165(3–4):265–287MathSciNetCrossRefGoogle Scholar
  45. Zhao XR, Hu BQ (2015) Fuzzy and interval-valued decision-theoretic rough set approaches based on the fuzzy probability measure. Inf Sci 298:534–554MathSciNetCrossRefGoogle Scholar
  46. Zhao XR, Hu BQ (2016) Fuzzy probabilistic rough sets and their corresponding three-way decisions. Knowl-Based Syst 91:126–142CrossRefGoogle Scholar
  47. Zhao SY, Tsang CC, Chen DG (2009) The model of fuzzy variable precision rough sets. IEEE Trans Fuzzy Syst 17(2):451–467CrossRefGoogle Scholar
  48. Zhao SY, Chen H, Li CP, Zhai MY (2013) RFRR—robust fuzzy rough reduction. IEEE Trans Fuzzy Syst 21(5):825–841CrossRefGoogle Scholar
  49. Ziarko W (2002) Set approximation quality measures in the variable precision rough set model. In: Proceedings of the 2nd International Conference on Hybrid Intelligent Systems (HIS”02). Soft Comput Syst 87:442–452Google Scholar
  50. Ziarko W (2008) Probabilistic approach to rough sets. Int J Approx Reason 49:272–284MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Bhalukdungri Jr. High SchoolRaigara, PuruliaIndia
  2. 2.Department of Pure and Applied MathematicsGuru Ghasidas UniversityBilaspurIndia

Personalised recommendations