Abstract
A new extended dominance relation is proposed for multi-attribute decision making problems with preference and incomplete information. First, the concept of new extended dominance relation based on the possibility of dominance relation between two objects is proposed. It substitutes the possibility of dominance relation for the conditions of limited extended dominance relation. In addition, it restricts that attribute values of two objects are missing in the same attribute. Through using probabilistic rough set theory, the threshold for the new extended dominance relation is estimated. It is decided by the loss regarding the risk or cost of those classification actions with respect to different states. Finally, the effectiveness of the new extended dominance relation is validated by experimental studies.
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References
Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129, 1–47 (2001)
Gao, Y., Zheng, G.L.: Extended rough sets based on variable-precision tolerance relation. Systems Engineering and Electronics 30, 477–480 (2008) (in Chinese)
He, Y.Q., Hu, S.S.: Rough analysis method of multi-attribute decision making with incomplete information. Journal of Systems Engineering 19, 117–120 (2004) (in Chinese)
Hu, M.L., Liu, S.F.: An analysis method of rough multi-attribute decision making based on limited extended dominance relation. Systems engineering 24, 106–110 (2006) (in Chinese)
Hu, M.L., Liu, S.F.: Rough analysis method of multi-attribute decision making based on generalized extended dominance relation. Control and Decision 22, 1347–1351 (2007) (in Chinese)
Ji, X., Li, L.S., Chen, S.B.: A new extended rough set model based on the dynamic tolerance relation and improved tolerance degree calculating method. In: Information Processing, APCIP 2009, pp. 94–96. IEEE Press, Los Alamitos (2009)
Luo, G.Z., Yang, X.J., Zhou, D.Q.: Rough analysis model of multi-attribute decision making based on limited extended dominance relation. Journal of Systems & Management 18, 391–396 (2009) (in Chinese)
Luo, G.Z., Yang, X.J.: Rough analysis model of multi-attribute decision making based on limited similarity dominance relation. Systems Engineering-Theory & Practice 29, 134–140 (2009) (in Chinese)
Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rudiments of rough sets. Information Sciences 177, 3–27 (2007)
Stefanowski, J., Tsoukias, A.: On the Extension of Rough Sets under Incomplete Information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–82. Springer, Heidelberg (1999)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-machine Studies 37(6), 793–809 (1992)
Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49(2), 255–271 (2008)
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Liang, D., Yang, S.X., Jiang, C., Zheng, X., Liu, D. (2010). A New Extended Dominance Relation Approach Based on Probabilistic Rough Set Theory. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds) Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science(), vol 6401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16248-0_28
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DOI: https://doi.org/10.1007/978-3-642-16248-0_28
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