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Decision-Oriented Rough Set Methods

  • Jiye LiangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9437)

Abstract

Rough set theory is a very effective multi-attribute decision analysis tool. The paper reviews four decision-oriented rough set models and methods: dominance-based rough set, three-way decisions, multigranulation decision-theoretic rough set and rough set based multi-attribute group decision-making model. We also introduce some of our group’s works under these four models. Several future research directions of decision-oriented rough sets are presented in the end of the paper.

Keywords

Rough set Multi-attribute decision making Group decision making 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 61432011, U1435212), Research Project Supported by Shanxi Scholarship Council of China (No. 2013-101), the Key Problems in Science and Technology Project of Shanxi Province (No. 20110321027-01) and the Construction Project of the Science and Technology Basic Condition Platform of Shanxi Province (No. 2012091002-0101).

References

  1. 1.
    Zopounidis, C., Doumpos, M.: Multicriteria classification and sorting methods: a literature review. Eur. J. Oper. Res. 138, 229–246 (2002)CrossRefGoogle Scholar
  2. 2.
    Hwang, C.L., Yoon, K.: Multiple Attribute Decision Making-Methods and Applications: A State of the Art Survey. Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, New York (1981)CrossRefGoogle Scholar
  3. 3.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, Now York (1980)zbMATHGoogle Scholar
  4. 4.
    Benayoun, R., Roy, B., Sussman, N.: Manual de refrence du programme electre. Note de Synthese et Formation, No. 25. Paris: Direction Scientifique SEMA (1966)Google Scholar
  5. 5.
    Brans, J.P., Mareschal, B.: The promethee vi procedure: how to differentiate hard from soft multicriteria problems. J. Decis. Syst. 4, 213–223 (1995)CrossRefGoogle Scholar
  6. 6.
    Hwang, C.L., Lai, Y.J., Liu, T.Y.: A new approach for multiple objective decision making. Comput. Oper. Res. 20, 889–899 (1993)CrossRefGoogle Scholar
  7. 7.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRefGoogle Scholar
  8. 8.
    Pawkak, Z.: Rough set approach to knowledge-based decision support. Eur. J. Oper. Res. 99, 48–57 (1997)CrossRefGoogle Scholar
  9. 9.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston (1991)CrossRefGoogle Scholar
  10. 10.
    Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation of a preference relation by dominance relations. Eur. J. Oper. Res. 117, 63–83 (1999)CrossRefGoogle Scholar
  11. 11.
    Skowron, A., Rauszer, C.: The Discernibility Matrices and Functions in Information Systems. In: Slowinski, R. (eds.) Intelligent Decision Support - Handbook of Applications and Advances of the Rough Sets Theory, vol. 11, pp. 331–362. Springer (1991)Google Scholar
  12. 12.
    Wang, G.Y., Yu, H., Yang, D.C.: Decision table reduction based on conditional information entropy. Chin. J. Comput. 25, 759–766 (2002)MathSciNetGoogle Scholar
  13. 13.
    Liang, J.Y., Wang, F., Dang, C.Y., Qian, Y.H.: An efficient rough feature selection algorithm with a multi-granulation view. Int. J. Approx. Reason. 53, 912–926 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liang, J.Y., Wang, F., Dang, C.Y., Qian, Y.H.: A group incremental approach to feature selection applying rough set technique. IEEE Trans. Knowl. Data Eng. 26, 294–308 (2014)CrossRefGoogle Scholar
  15. 15.
    Slezak, D.: Approximate entropy reducts. Fund. Inform. 53, 365–390 (2002)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Grzymala-Busse, J.W.: LERS: A system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Set theory, vol. 11, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)CrossRefGoogle Scholar
  17. 17.
    Greco, S., Matarazzo, B., Slowinski, R.: The use of rough sets and fuzzy sets in MCDM. In: Gal, T., Hanne, T., Stewart, T. (eds.) Advances in Multiple Criteria decision Making. Kluwer Academic Publishers, Dordrecht (1999)zbMATHGoogle Scholar
  18. 18.
    Grzymala-Busse, J.W., Stefanowski, J.: Three discretization methods for rule induction. Int. J. Intell. Syst. 26, 29–38 (2001)CrossRefGoogle Scholar
  19. 19.
    Leung, Y., Fischer, M.M., Wu, W.Z., Mi, J.S.: A rough set approach for the discovery of classification rules in interval-valued information systems. Int. J. Approx. Reason. 47, 233–246 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1990)CrossRefGoogle Scholar
  21. 21.
    Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, vol. 11, pp. 203–232. Kluwer Academic Publishers, Dordrecht (1992)CrossRefGoogle Scholar
  22. 22.
    Hu, Q.H., Xie, Z.X., Yu, D.R.: Hybrid attribute reduction based on a novel fuzzy rough model and information granulation. Pattern Recogn. 40, 3509–3521 (2007)CrossRefGoogle Scholar
  23. 23.
    Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129, 1–7 (2001)CrossRefGoogle Scholar
  24. 24.
    Greco, S., Matarazzo, B., Slowinski, R.: Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur. J. Oper. Res. 138, 247–259 (2002)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Greco, S., Matarazzo, B., Slowinski, R., Zanakis, S.: Global investing risk: a case study of knowledge assessment via rough sets. Annal Oper. Res. 185, 105–138 (2011)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Greco, S., Slowinski, R., Zielniewicz, P.: Putting dominance-based rough set approach and robust ordinal regression together. Dec. Support Syst. 54, 891–903 (2013)CrossRefGoogle Scholar
  27. 27.
    Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy set model. Fuzzy Sets Syst. 21, 357–362 (1987)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. Int. J. Man-Mach. Stud. 29, 81–95 (1988)CrossRefGoogle Scholar
  29. 29.
    Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Yao, Y.Y., Wong, S.K.M.: A decisoin theoretic framework for approximating concepts. Int. J. Man-Mach. Stud. 37, 793–809 (1992)CrossRefGoogle Scholar
  31. 31.
    Yao, Y.Y., Zhou, B.: Naive Bayesian Rough Sets. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS (LNAI), vol. 6401, pp. 719–726. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  32. 32.
    Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Inf. Sci. 152, 217–230 (2003)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Qian, Y.H., Liang, J.Y., Yao, Y.Y., Dang, C.Y.: MGRS: A multi-granulation rough set. Inf. Sci. 180, 949–970 (2010)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Yang, X.B., Song, X.N., Chen, Z.H., Yang, J.Y.: On multi-granulation rough sets in incomplete information system. Int. J. Mach. Learn. Cyber. 3, 223–232 (2011)CrossRefGoogle Scholar
  35. 35.
    Xu, W.H., Sun, W.X., Zhang, X.Y., Zhang, W.X.: Multiple granulation rough set approach to ordered information systems. Inter. J. General Syst. 41, 475–501 (2012)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Lin, G.P., Liang, J.Y., Qian, Y.H.: Multigranulation rough sets: from partition to covering. Inf. Sci. 241, 101–118 (2013)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Liou, J.J.H., Tzeng, G.H.: A dominance-based rough set approach to customer behavior in the airline market. Inf. Sci. 180, 2230–2238 (2010)CrossRefGoogle Scholar
  38. 38.
    Hu, Q.H., Yu, D.R., Guo, M.Z.: Fuzzy preference based rough sets. Inf. Sci. 180, 2003–2022 (2010)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Szelag, M., Greco, S., Slowinski, R.: Variable consistency dominance-based rough set approach to preference learning in multicriteria ranking. Inf. Sci. 277, 525–552 (2014)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Song, P., Liang, J.Y., Qian, Y.H.: A two-grade approach to ranking interval data. Knowl.-Based Syst. 27, 234–244 (2012)CrossRefGoogle Scholar
  41. 41.
    Yao, Y.Y.: An Outline of a Theory of Three-Way Decisions. In: Yao, J., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1–17. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  42. 42.
    Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, vol. 5, pp. 17–25. North-Holland, New York (1990)Google Scholar
  43. 43.
    Greco, S., Słowiński, R., Yao, Y.Y.: Bayesian Decision Theory for Dominance-Based Rough Set Approach. In: Yao, J.T., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślȩzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 134–141. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  44. 44.
    Herbert, J.P., Yao, J.T.: Game-Theoretic Risk Analysis in Decision-Theoretic Rough Sets. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 132–139. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  45. 45.
    Liang, D.C., Liu, D.: Deriving three-way decisions from intuitionistic fuzzy decision theoretic rough sets. Inf. Sci. 200, 28–48 (2015)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Yao, Y.Y.: Granular Computing and Sequential Three-Way Decisions. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013. LNCS (LNAI), vol. 8171, pp. 16–27. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  47. 47.
    Wang, B.L., Liang, J.Y.: A Novel Intelligent Multi-attribute Three-Way Group Sorting Method Based on Dempster-Shafer Theory. In: Miao, D.Q., Pedrycz, W., Slezak, D., Peters, G., Hu, Q., Wang, R. (eds.) RSKT 2014. LNCS (LNAI), vol. 8818, pp. 789–800. Springer, Heidelberg (2014) Google Scholar
  48. 48.
    Qian, Y.H., Zhang, H., Sang, Y.L., Liang, J.Y.: Multi-granulation decision-theoretic rough sets. Int. J. Approx. Reason. 55, 225–237 (2014)CrossRefGoogle Scholar
  49. 49.
    Liang, J.Y., Wang, B.L.: Rough set based multi-attribute group decision making model. In: Jia, X.Y., Shang, L., Zhou X. Z. et al. Three-way Decision Theory and Applications, pp. 131–148. Nanjing University Press, Nanjing (2012)Google Scholar
  50. 50.
    Pang, J.F., Liang, J.Y.: Evaluation of the results of multi-attribute group decision-making with linguistic information. OMEGA 40, 294–301 (2012)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyTaiyuan Normal UniversityJinzhongChina
  2. 2.Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of EducationShanxi UniversityTaiyuanChina

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