Decision-Theoretic Rough Set Attribute Reduction and Classification Based on Fuzzification
GUO Min1, JIA Xiu-Yi2, SHANG Lin1
1State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093 2School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094
Abstract：The decision-theoretic rough set (DTRS) is a kind of probabilistic rough set model with certain tolerance based on the Bayesian risk minimization principle. However, the current research on DTRS model is restricted to processing information tables with discrete data. In this paper, the decision-theoretic rough set theory is combined with fuzzy sets, and the fuzzy membership functions are employed to replace the posterior probability calculating method when calculating the expected risk losses in the DTRS model. Thus, the new decision rules are derived to effectively deal with the information system with continuous data. Experiments show that the proposed method is feasible and it has a better classification performance by adjusting the membership functions.
[1] Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356 [2] Wang G Y, Yao Y Y, Yu H. A Survey on Rough Set Theory and Applications. Chinese Journal of Computers, 2009, 32(7): 1229-1246 (in Chinese) (王国胤,姚一豫,于 洪.粗糙集理论与应用研究综述.计算机学报, 2009, 32(7): 1229-1246) [3] Pawlak Z, Wong S K M, Ziarko W. Rough Sets: Probabilistic versus Deterministic Approach. International Journal of Man-Machine Studies, 1988, 29(1): 81-95 [4] Ziarko W. Variable Precision Rough Set Model. Journal of Computer and System Sciences, 1993, 46(1): 39-59 [5] S＇lzak D. Rough Sets and Bayes Factor // Peters J F, Skowron A, eds. Trans on Rough Sets III. Berlin, Germany: Springer, 2005, 3400: 202-229 [6] S＇lzak D, Ziarko W. The Investigation of the Bayesian Rough Set Model. International Journal of Approximate Reasoning, 2005, 40(1/2): 81-91 [7] Yao Y Y. Decision-Theoretic Rough Set Models // Proc of the 2nd International Conference on Rough Sets and Knowledge Technology. Toronto, Canada, 2007: 1-12 [8] Yao Y Y, Wong S K M. A Decision Theoretic Framework for Approximating Concepts. International Journal of Man-Machine Studies, 1992, 37(6): 793-809 [9] Yao Y Y. Three-Way Decisions with Probabilistic Rough Sets. Information Sciences, 2010, 180(3): 341-353 [10] Jensen R, Shen Q. New Approaches to Fuzzy-Rough Feature Selection. IEEE Trans on Fuzzy Systems, 2009, 17(4): 824-838 [11] Jensen R, Shen Q. Fuzzy-Rough Attribute Reduction with Application to Web Categorization. Fuzzy Sets and Systems, 2004, 141(3): 469-485 [12] Tsang E C C, Chen D G, Yeung D S, et al. Attributes Reduction Using Fuzzy Rough Sets. IEEE Trans on Fuzzy Systems, 2008, 16(5): 1130-1141 [13] Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338-353 [14] Zhao J, Bose B K. Evaluation of Membership Functions for Fuzzy Logic Controlled Induction Motor Drive // Proc of the 28th IEEE Annual Conference of the Industrial Electronics Society. Sevilla, Spain, 2002, I: 229-234 [15] Dubois D, Prade H. Twofold Fuzzy Sets and Rough Sets-Some Issues in Knowledge Representation. Fuzzy Sets and Systems, 1987, 23(1): 3-18 [16] Dubois D, Prade H. Putting Rough Sets and Fuzzy Sets Together // Slowiriski R, ed. Handbook of Applications and advances of the Rough Sets Theory. Heidelberg, Germany: Springer, 1992: 203-232 [17] Jensen R, Cornelis C. Fuzzy-Rough Nearest Neighbour Classification and Prediction. Theoretical Computer Science, 2011, 412(42): 5871-5884 [18] Li H X, Zhou X Z, Zhao J B, et al. Attribute Reduction in Decision-Theoretic Rough Set Model: A Further Investigation // Proc of the 6th International Conference on Rough Sets and Knowledge Technology. Banff, Canada, 2011: 466-475
2014, Vol. 27 
