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Multi-decision-makers-based Monotonic Variable Consistency Rough Set Approach with Multiple Attributes and Criteria

  • Wenbin Pei
  • He LinEmail author
  • Li Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9437)

Abstract

The paper separates decision expression system into three parts: the relation system, the decision-making system and the causal system by the perspective of Pansystems theory. In these three separated systems, the extended approach involves multiple types of attributes and many decision-makers, and it aims at modelling data expressed by monotonic variable consistency measures. Furthermore, the two referred thresholds, according to Bayes decision procedure that is applied by Decision Theoretic Rough Set, can be calculated directly. So the paper proposes Multi-decision-makers-based Monotonic Variable Consistency Rough Set Approach with Multiple Attributes and Criteria, and its properties are proposed and proved.

Keywords

Monotonicity Multiple types of attributes and criteria Many decision-makers Rough set Pansystems theory 

Notes

Acknowledgement

The paper is supported by the Fundamental Research Funds for the Central Universities(lzujbky-2012-43). The authors thank valued amendments which are raised by Professor Yongli Li.

References

  1. 1.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRefGoogle Scholar
  2. 2.
    Pawlak, Z.: Rough sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefGoogle Scholar
  3. 3.
    Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Trans. Knowl. Data Eng. 12, 331–336 (2000)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    Wu, X.M.: Views to World from Pansystem. The Renmin University of China Press, Beijing (1990)Google Scholar
  6. 6.
    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
  7. 7.
    Fortemps, P., Greco, S., Slowinski, R.: Multicriteria decision support using rules that represent rough-graded preference relation. Eur. J. Oper. Res. 188, 206–223 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ziarko, W.: Variable precision rough sets model. J. Comput. Syst. Sci. 46, 39–59 (1993)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Blaszczynski, J., Greco, S., Slowinski, R., Szelag, M.: Monotonic variable consistency rough set approaches. Int. J. Approximate Reasoning 50, 979–999 (2009)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Greco, S., Pawlak, Z., Slowinski, R.: Can bayesian confirmation measures be useful for rough set decision rules? Eng, Appl. Artif. Intell. 17, 345–361 (2004)CrossRefGoogle Scholar
  11. 11.
    Greco, S., Matarazzo, B., Slowinski, R.: Rough membership and bayesian confirmation measures for parameterized rough sets. Int. J. Approximate Reasoning 49, 285–300 (2008)CrossRefGoogle Scholar
  12. 12.
    Slowinski, R., Stefanowski, J., Greco, S., Matarazzo, B.: Rough sets based processing of inconsistent information in decision analysis. Control Cybern. 29, 379–404 (2000)zbMATHGoogle Scholar
  13. 13.
    Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 111, 239–259 (1998)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach on pairwise comparison tables to decision involving multiple decision makers. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 126–135. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  15. 15.
    Greco, S., Mousseau, V., Slowinski, R.: Ordinal regression revisited: multiple criteria ranking with a set of additive value functions. Eur. J. Oper. Res. 191, 415–435 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Slowinski, R.: Rough set learning of preferential attitude in multi-criteria decision making. In: Komorowski, J. (ed.) Methodologies Intell. Syst., vol. 689, pp. 642–651. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  17. 17.
    Yao, Y.Y.: Granular computing. Comput. Sci. 31, 1–5 (2004)Google Scholar
  18. 18.
    Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 111, 239–259 (1998)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Miao, D.Q., Li, D.T., Yao, Y.Y.: Uncertainty and Granular Computing. Science Press, Beijing (2011)Google Scholar
  20. 20.
    Liu, D., Li, T.R., Li, H.X.: Interval-valued decision-theoretic rough sets. Comput. Sci. 39, 179–182 (2012)Google Scholar
  21. 21.
    Yao, Y.: Decision-theoretic rough set models. 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. 1–12. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  22. 22.
    Pedrycz, W.: Granular Computing: Analysis and Design of Intelligent Systems. CRC Press/Francis Taylor, Boca Raton (2013) CrossRefGoogle Scholar
  23. 23.
    Li, W., Xu, W.: Probabilistic rough set model based on dominance relation. In: Miao, D., Pedrycz, W., Slezak, D., Peters, G., Hu, Q., Wang, R. (eds.) RSKT 2014. LNCS, vol. 8818, pp. 856–864. Springer, Heidelberg (2014) Google Scholar
  24. 24.
    Li, W.T., Xu, W.H.: Multigranulation decision-theoretic rough set in ordered information system. Fundamenta Informaticae 139, 67–89 (2015)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Greco, S., Matarazzo, B., Słowiński, R., Stefanowski, J.: Variable consistency model of dominance-based rough sets approach. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 170–181. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  26. 26.
    Greco, S., Matarazzo, B., Slowinski, R.: Dominance-based rough set approach as a proper way of handling graduality in rough set theory. Trans. Rough Sets 4400, 36–52 (2007)MathSciNetzbMATHGoogle Scholar
  27. 27.
    Greco, S., Słowiński, R., Yao, 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
  28. 28.
    Qian, Y., Zhang, H.H., Sang, Y.L., Liang, J.Y.: Multigranulation decision-theoretic rough sets. Int. J. Approximate Reasoning 55(1), 225–237 (2014)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Li, Y.L., Lin, Y., Wang, X.Y., Lin, H.: An initial comparision of fuzzy sets and rough sets from the view of pansystem theory. In: Hu, X.H., Liu, Q., Skowron, A. (eds) IEEE International Conference on Granular Computing, vol. 2, pp. 520–525 (2005)Google Scholar
  30. 30.
    Pei, W.B., Lin, H., Li, L.Y.: Optimal-neighborhood statistics rough set approach with multiple attributes and criteria. In: Miao, D., Pedrycz, W., Slezak, D., Peters, G., Hu, Q., Wang, R. (eds.) RSKT 2014. LNCS, vol. 8818, pp. 683–692. Springer, Heidelberg (2014) Google Scholar

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Authors and Affiliations

  1. 1.School of Information Science and EngineeringLanZhou UniversityLanzhouPeople’s Republic of China

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