Decision-theoretic Rough Sets in Incomplete Information System

• Autorzy: Yang X. , Lu Z. , Li T-J.
• Języki publikacji: EN

Abstrakty

EN

Decision-theoretic rough sets in two kinds of incomplete information systems are discussed in this paper. One is for the classical decision attribute and the other for the fuzzy decision attribute. In complete information system, the universe is partitioned with the equivalence relation. Given a concept, we get a pair of approximations of the concept using rough set theory, and the universe can be partitioned into three regions for making a decision. An incomplete information table can be expressed as a family of complete information tables. The universe is partitioned by the equivalence relation for each complete information table. The probability of each object belonging to the concept can be calculated in a completion from incomplete information system, and then the total probability of the object belonging to the concept can be obtained. Decision rules are derived using total probability instead of conditional probability in decision-theoretic rough sets. Finally, the universe is divided into three regions according to the total probability. A similar approach to fuzzy incomplete information system is examined and the universe is also divided into three regions.

Słowa kluczowe

EN

fuzzy information system; fuzzy rough sets; incomplete information system; membership degree; probability

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 126, nr 4
• Strony: 353--375
• Opis fizyczny: Bibliogr. 34 poz., tab.

Twórcy

autor

Yang X.

• School of Mathematics, Physics & Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, P. R. China, 316004

autor

Lu Z.

• School of Mathematics, Physics & Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, P. R. China, 316004

autor

Li T-J.

• School of Mathematics, Physics & Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, P. R. China, 316004

Bibliografia

• [1] Dembczynski, K., Greco, S., Slowinski, R.: Rough set approach to multiple criteria classification with imprecise evaluations and assignments, European Journal of Operational Research, 198, 2009, 626-636.
• [2] Herbert, J.P., Yao, J.T.: Game-theoretic rough sets, Fundamenta Informaticae, 108, 2011, 267-286.
• [3] Herbert, J.P., Yao, J.T.: Analysis of data-driven parameters in Game-theoretic rough sets, Proc. Rough Sets and Knowledge Technology (J.T. Yao, S. Ramanna, G. Wang, Z. Suraj, Eds.), LNCS (LNAI), 6954, Springer- Heidelberg, 2011, 447-456.
• [4] Jia, X.Y., Zheng, K., Li, W.W., Liu, T.T., Shang, L.: Three-way decisions solution to filter spam email: an empirical study, Proc. 8th International Conference on Rough Sets and Current Trends in Computing, 2012, 287-296.
• [5] Jia, X., Li, W., Shang, L., Chen, J.: An optimization viewpoint of decision-theoretic rough set model, Proc. Rough Sets and Knowledge Technology (J.T. Yao, S. Ramanna, G. Wang, Z. Suraj, Eds.), LNCS (LNAI), 6954, Springer-Heidelberg, 2011, 457-4265.
• [6] Kryszkiewicz, M.: Rough set approach to incomplete information systems, Information Sciences, 112, 1998, 39-49.
• [7] Kryszkiewicz, M.: Rules in incomplete information systems, Information Sciences, 113, 1999, 271-292.
• [8] Leung, Y., Wu, W.-Z., Zhang, W.-X.: Knowledge acquisition in incomplete information systems: A rough set appproach, European Journal of Operational Research, 168, 2006, 164-180.
• [9] Lingras, P., Yao, Y.Y.: Data mining using extensions of the rough set model, Journal of the American Society for Information Science, 49, 1998, 415-422.
• [10] Li, D.Y., Zhang, B., Leung, Y.: On knowledge reduction in inconsistent decision information systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12, 2004, 651-672.
• [11] Li, H.X., Zhou, X.Z.: Risk decision making based on decision-theoretic rough set: a three-way view decision model, International Journal of Computational Intelligence Systems, 4(1), 2011, 1-11.
• [12] Li, H.X., Wang M.H., Zhou, X.Z., Zhao J.B.: An interval set model for learning rules from incomplete information table, International Journal of Approximate Reasoning, 53(1), 2012, 24-37.
• [13] Li, H.X., Yao Y.Y., Zhou, X.Z., Huang, B.: A two-phase model for learning rules from incomplete data, Fundamenta Informaticae, 94(2), 2009, 219-232.
• [14] Li, H.X., Zhou, X.Z., Zhao, J.B, Liu, D.: Non-monotonic attribute reduction in decision-theoretic rough sets, Fundamenta Informaticae, 2013.
• [15] Li, R.P., Yao, Y.Y.: Indiscernibility and similarity in an incomplete information table, Proc. Rough Sets and Knowledge Technology (J. Yu, S. Greco, P. Lingras, G. Wang, A. Skowron, Eds.), LNCS (LNAI), 6401, Springer-Heidelberg, 2010, 110-117.
• [16] Liu, D., Yao, Y.Y., Li, T.R.: Three-way investment decisions with decision-theoretic rough sets, International Journal of Computational Intelligence Systems, 4(1), 2011, 66-74.
• [17] Liu, D., Li, T.R., Ruan, D.: Probabilistic model criteria with decision-theoretic rough sets, Information Sciences, 181, 2011, 3709-3722.
• [18] Liu, D., Li, T., Li, H.: A multiple-category classification approach with decision-theoretic rough sets, Fundamenta Informaticae, 115, 2012, 173-188.
• [19] Mi, J.S., Wu, W.Z., Zhang, W.X.: Approaches to knowledge reductions based on variable precision rough sets mode, Information Sciences, 159, 2004, 255-274.
• [20] Pawlak, Z.: Rough sets, International Journal of Computer and Information Sciences, 11, 1982, 341-356.
• [21] Wu, W.Z.: Attribute reduction based on evidence theory in incomplete decision systems, Information Sciences, 178, 2008, 1355-1371.
• [22] Wu, W.Z.: Knowledge reduction in random incomplete information systems, Proc. Rough Sets and Knowledge Technology (J. Yu, S. Greco, P. Lingras, G. Wang, A. Skowron, Eds.), LNCS (LNAI), 6401, Springer- Heidelberg, 2010, 38-45.
• [23] Wu, W.Z.: Knowledge reduction in random incomplete information systems via evidence theory, Fundamenta Informaticae, 115, 2012, 203-218.
• [24] Yang, X.P.: Fuzziness in incomplete information systems, Proceedings of the Third International Conference on Machine Learning and Cybernetics, Shanghai, 26-29 August 2004, 1599-1603.
• [25] Yang, X.P.: An interpretation of rough sets in incomplete information systems within intuitionistic fuzzy sets, Proc. Rough Sets and Knowledge Technology (P. Wen, et al. Eds.), LNCS (LNAI), 5589, Springer-Heidelberg, 2010, 326-333.
• [26] Yang, X.P., Yao, J.T.: A multi-agent decision-theoretic rough set model, Proc. Rough Sets and Knowledge Technology (J. Yu, S. Greco, P. Lingras, G. Wang, A. Skowron, Eds.), LNCS (LNAI), 6401, Springer- Heidelberg, 2010, 711-718.
• [27] Yang, X.P., Yao, J.T.: Modelling multi-agent three-way decisions with decision-theoretic rough sets, Fundamenta Informaticae, 115, 2012, 157-171.
• [28] Yang, X.P., Song, H.G., Li, T.J.: Decision making in incomplete information system based on decision- theoretic rough sets, Proc. Rough Sets and Knowledge Technology (J.T. Yao, S. Ramanna, G. Wang, Z. Suraj, Eds.), LNCS (LNAI), 6954, Springer-Heidelberg, 2011,495-503.
• [29] Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set models, Proc. 5th Int. Symposium on Methodologies for Intelligent Systems (Z. W. Ras, M. Zemankova, M. L. Emrich, Eds.), 5, 1990, 17-24.
• [30] Yao, Y.Y.: Probabilistic approaches to rough sets, Expert Systems, 20, 2003, 287-297.
• [31] Yao, Y.Y.: Three-way decisions with probabilistic rough sets, Information Sciences, 180, 2010, 341-353.
• [32] Yu, H., Chu, S., Yang, D.: Autonomous Knowledge-oriented clustering using decision-theoretic rough set theory, Fundamenta Informaticae, 115, 2012, 141-156.
• [33] Zhang, W.X., Leung, Y., Wu, W.Z.: Information System and Knowledge Discovery, Science Press, Beijing 2003.
• [34] Ziarko, W.: Variable precision rough set model, Journal of Computer and System Science, 46, 1993, 39-59.