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Dominance-based fuzzy rough approach to an interval-valued decision system

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Abstract

Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance principle in terms of pairs of objects. In this paper, a ranking method of interval-valued data is used to describe the degree of dominance in the interval-valued information system. Therefore, the fuzzy rough technique is employed to construct the rough approximations of upward and downward unions of decision classes, from which one can induce at least and at most decision rules with certainty factors from the interval-valued decision system. Some numerical examples are employed to substantiate the conceptual arguments.

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References

  1. Pawlak Z. Rough Sets-Theoretical Aspects of Reasoning About Data. Boston: Kluwer Academic Publishers Press, 1991

    MATH  Google Scholar 

  2. Greco S, Matarazzo B, Słowiński R. Rough approximation by dominance relations. International Journal of Intelligent Systems, 2002, 17(2): 153–171

    Article  MATH  Google Scholar 

  3. Greco S, Matarazzo B, Słowiński R. Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 2001, 129(1): 1–47

    Article  MathSciNet  MATH  Google Scholar 

  4. Błaszczyński J, Greco S, Słowiński R. Multi-criteria classification-a new scheme for application of dominance-based decision rules. European Journal of Operational Research, 2007, 181(3): 1030–1044

    Article  MATH  Google Scholar 

  5. Yang X, Yang J, Wu C, Yu D. Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Information Sciences, 2008, 178(4): 1219–1234

    Article  MathSciNet  MATH  Google Scholar 

  6. Yang X, Xie J, Song X, Yang J. Credible rules in incomplete decision system based on descriptors. Knowledge-Based Systems, 2009, 22(1): 8–17

    Article  Google Scholar 

  7. Yang X, Yu D, Yang J, Wei L. Dominance-based rough set approach to incomplete interval-valued information system. Data & Knowledge Engineering, 2009, 68(11): 1331–1347

    Article  Google Scholar 

  8. Shao M, Zhang W. Dominance relation and rules in an incomplete ordered information system. International Journal of Intelligent Systems, 2005, 20(1): 13–27

    Article  MATH  Google Scholar 

  9. Greco S, Inuiguchi M, Słowiński R. Fuzzy rough sets and multiple-premise gradual decision rules. International Journal of Approximate Reasoning, 2006, 41(2): 179–211

    Article  MathSciNet  MATH  Google Scholar 

  10. Greco S, Matarazzo B, Słowiński R. Dominance-based rough set approach to case-based reasoning. In: Proceedings of 3rd International Conference on Modeling Decisions for Artificial Intelligence. 2006, 7–18

  11. Greco S, Matarazzo B, Słowiński R. Fuzzy set extensions of the dominance-based rough set approach. In: Sola H, Herrera F, Montero J, eds. Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Berlin: Springer-Verlag, 2008, 239–261

    Chapter  Google Scholar 

  12. Błaszczyński J, Greco S, Słowiński R. On variable consistency dominance-based rough set approaches. In: Proceedings of 5th International Conference on Rough Sets and Current Trends in Computing. 2006, 191–202

  13. Błaszczyński J, Greco S, Słowiński R. Monotonic variable consistency rough set approaches. In: Proceedings of 2nd International Conference on Rough Sets and Knowledge Technology. 2007, 126–133

  14. Qian Y, Dang C, Liang J, Tang D. Set-valued ordered information systems. Information Sciences, 2009, 179(16): 2809–2832

    Article  MathSciNet  MATH  Google Scholar 

  15. Fan T, Liu D, Tzeng G. Rough set-based logics for multicriteria decision analysis. European Journal of Operational Research, 2007, 182(1): 340–355

    Article  MathSciNet  MATH  Google Scholar 

  16. Qian Y, Liang J, Dang C. Interval ordered information systems. Computers & Mathematics with Applications, 2008, 56(8): 1994–2009

    Article  MathSciNet  MATH  Google Scholar 

  17. Dembczyński K, Greco S, Słowiński R. Rough set approach to multiple criteria classification with imprecise evaluations and assignments. European Journal of Operational Research, 2009, 198(2): 626–636

    Article  MathSciNet  MATH  Google Scholar 

  18. Da Q, Liu X. Interval number linear programming and its satisfactory solution. Systems Engineering — Theory & Practice, 1999, 19(4): 3–7

    Google Scholar 

  19. Facchinetti G, Ricci R, Muzzioli S. Note on ranking fuzzy triangular numbers. International Journal of Intelligent Systems, 1998, 13(7): 613–622

    Article  Google Scholar 

  20. Sengupta A, Pal T. On comparing interval numbers. European Journal of Operational Research, 2000, 127(1): 28–43

    Article  MathSciNet  MATH  Google Scholar 

  21. Bhatt R, Gopal M. On the compact computational domain of fuzzy-rough sets. Pattern Recognition Letters, 2005, 26(11): 1632–1640

    Article  Google Scholar 

  22. Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 1990, 17(2): 191–209

    Article  MATH  Google Scholar 

  23. Li T. Rough approximation operators on two universes of discourse and their fuzzy extensions. Fuzzy Sets and Systems, 2008, 159(22): 3033–3050

    Article  MathSciNet  MATH  Google Scholar 

  24. Nanda S, Majumdar S. Fuzzy rough sets. Fuzzy Sets and Systems, 1992, 45(2): 157–160

    Article  MathSciNet  MATH  Google Scholar 

  25. Wu W, Mi J, Zhang W. Generalized fuzzy rough sets. Information Sciences, 2003, 151: 263–282

    Article  MathSciNet  MATH  Google Scholar 

  26. Wu W, Zhang W. Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences, 2004, 159(3–4): 233–254

    Article  MathSciNet  MATH  Google Scholar 

  27. Wu W, Leung Y, Mi J. On characterizations of (T, J)-fuzzy rough approximation operators. Fuzzy Sets and Systems, 2005, 154(1): 76–102

    Article  MathSciNet  MATH  Google Scholar 

  28. Yeung D, Chen D, Tsang E, Lee J, Wang X. On the generalization of fuzzy rough sets. IEEE Transactions on Fuzzy Systems, 2005, 13(3): 343–361

    Article  Google Scholar 

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Correspondence to Xibei Yang.

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Yang, X., Zhang, M. Dominance-based fuzzy rough approach to an interval-valued decision system. Front. Comput. Sci. China 5, 195–204 (2011). https://doi.org/10.1007/s11704-011-0331-4

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