Consistency-preserving attribute reduction in fuzzy rough set framework

Attribute reduction (feature selection) has become an important challenge in areas of pattern recognition, machine learning, data mining and knowledge discovery. Based on attribute reduction, one can extract fuzzy decision rules from a fuzzy decision table. As consistency is one of several criteria for evaluating the decision performance of a decision-rule set, in this paper, we devote to present a consistency-preserving attribute reduction in fuzzy rough set framework. Through constructing the membership function of an object, we first introduce a consistency measure to assess the consistencies of a fuzzy target set and a fuzzy decision table, which underlies a foundation for attribute reduction algorithm. Then, we derive two attribute significance measures based on the proposed consistency measure and design a forward greedy algorithm (ARBC) for attribute reduction from both numerical and nominal data sets. Numerical experiments show the validity of the proposed algorithm from search strategy and heuristic function in the meaning of consistency. Number of the selected features is the least for a given threshold of consistency measure.

[1]  Yee Leung,et al.  Granular Computing and Knowledge Reduction in Formal Contexts , 2009, IEEE Transactions on Knowledge and Data Engineering.

[2]  William Zhu,et al.  Matroidal approaches to generalized rough sets based on relations , 2011, Int. J. Mach. Learn. Cybern..

[3]  Rajen B. Bhatt,et al.  On the compact computational domain of fuzzy-rough sets , 2005, Pattern Recognit. Lett..

[4]  Jiye Liang,et al.  Consistency measure, inclusion degree and fuzzy measure in decision tables , 2008, Fuzzy Sets Syst..

[5]  Yuming Zhou,et al.  An improved accuracy measure for rough sets , 2005, J. Comput. Syst. Sci..

[6]  Jiye Liang,et al.  Incomplete Multigranulation Rough Set , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[7]  Jiye Liang,et al.  A new method for measuring uncertainty and fuzziness in rough set theory , 2002, Int. J. Gen. Syst..

[8]  Jiye Liang,et al.  Inclusion degree: a perspective on measures for rough set data analysis , 2002, Inf. Sci..

[9]  Xizhao Wang,et al.  Induction of multiple fuzzy decision trees based on rough set technique , 2008, Inf. Sci..

[10]  Andrzej Skowron,et al.  Rough set methods in feature selection and recognition , 2003, Pattern Recognit. Lett..

[11]  Duoqian Miao,et al.  Hierarchical decision rules mining , 2010, Expert Syst. Appl..

[12]  T. Pavlenko.  On feature selection, curse-of-dimensionality and error probability in discriminant analysis , 2003 .

[13]  XIAOHUA Hu,et al.  LEARNING IN RELATIONAL DATABASES: A ROUGH SET APPROACH , 1995, Comput. Intell..

[14]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[15]  Ming-Wen Shao,et al.  Set approximations in fuzzy formal concept analysis , 2007, Fuzzy Sets Syst..

[16]  Xizhao Wang,et al.  Learning fuzzy rules from fuzzy samples based on rough set technique , 2007, Inf. Sci..

[17]  DEYU LI,et al.  On Knowledge Reduction In Inconsistent Decision Information Systems , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[18]  Qiang Shen,et al.  Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches , 2004, IEEE Transactions on Knowledge and Data Engineering.

[19]  Jiye Liang,et al.  Information entropy, rough entropy and knowledge granulation in incomplete information systems , 2006, Int. J. Gen. Syst..

[20]  Chong-Ho Choi,et al.  Input feature selection for classification problems , 2002, IEEE Trans. Neural Networks.

[21]  Wei Xu,et al.  Fuzzy inference based on fuzzy concept lattice , 2006, Fuzzy Sets Syst..

[22]  Wen-Xiu Zhang,et al.  A knowledge processing method for intelligent systems based on inclusion degree , 2003, Expert Syst. J. Knowl. Eng..

[23]  Y. H. Qian,et al.  Rough Set Method Based on Multi-Granulations , 2006, 2006 5th IEEE International Conference on Cognitive Informatics.

[24]  Shan Feng,et al.  Decision support for fuzzy comprehensive evaluation of urban development , 1999, Fuzzy Sets Syst..

[25]  Dominik Slezak,et al.  The investigation of the Bayesian rough set model , 2005, Int. J. Approx. Reason..

[26]  Jiye Liang,et al.  Converse approximation and rule extraction from decision tables in rough set theory , 2008, Comput. Math. Appl..

[27]  Wojciech Ziarko,et al.  Variable Precision Rough Set Model , 1993, J. Comput. Syst. Sci..

[28]  Marzena Kryszkiewicz,et al.  Rules in Incomplete Information Systems , 1999, Inf. Sci..

[29]  Andrzej Skowron,et al.  EXTRACTING LAWS FROM DECISION TABLES: A ROUGH SET APPROACH , 1995, Comput. Intell..

[30]  Rajen B. Bhatt,et al.  On fuzzy-rough sets approach to feature selection , 2005, Pattern Recognit. Lett..

[31]  Malcolm J. Beynon,et al.  Reducts within the variable precision rough sets model: A further investigation , 2001, Eur. J. Oper. Res..

[32]  Jiye Liang,et al.  On the evaluation of the decision performance of an incomplete decision table , 2008, Data Knowl. Eng..

[33]  Yee Leung,et al.  On Generalized Fuzzy Belief Functions in Infinite Spaces , 2009, IEEE Transactions on Fuzzy Systems.

[34]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[35]  Zheng Pei,et al.  Interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference , 2006, Inf. Sci..

[36]  Qiang Shen,et al.  Fuzzy-Rough Sets Assisted Attribute Selection , 2007, IEEE Transactions on Fuzzy Systems.

[37]  Marzena Kryszkiewicz,et al.  Rough Set Approach to Incomplete Information Systems , 1998, Inf. Sci..

[38]  Jiye Liang,et al.  Measures for evaluating the decision performance of a decision table in rough set theory , 2008, Inf. Sci..

[39]  Jiye Liang,et al.  Rough Set Approximation Based on Dynamic Granulation , 2005, RSFDGrC.

[40]  Zdzisław Pawlak,et al.  Can Bayesian confirmation measures be useful for rough set decision rules? , 2004, Eng. Appl. Artif. Intell..

[41]  Qinghua Hu,et al.  Uncertainty measures for fuzzy relations and their applications , 2007, Appl. Soft Comput..

[42]  Fei-Yue Wang,et al.  Reduction and axiomization of covering generalized rough sets , 2003, Inf. Sci..

[43]  Dominik Slezak,et al.  Approximate Entropy Reducts , 2002, Fundam. Informaticae.

[44]  Wei-Zhi Wu,et al.  Knowledge reduction in random information systems via Dempster-Shafer theory of evidence , 2005, Inf. Sci..

[45]  Wen-Xiu Zhang,et al.  Measuring roughness of generalized rough sets induced by a covering , 2007, Fuzzy Sets Syst..

[46]  Wei-Zhi Wu,et al.  Approaches to knowledge reduction based on variable precision rough set model , 2004, Inf. Sci..

[47]  Tzung-Pei Hong,et al.  Mining fuzzy β-certain and β-possible rules from quantitative data based on the variable precision rough-set model , 2007, Expert Syst. Appl..

[48]  Qinghua Hu,et al.  Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation , 2007, Pattern Recognit..

[49]  Mi Ju,et al.  Comparative Studies of Knowledge Reductions in Inconsistent Systems , 2003 .

[50]  Qinghua Hu,et al.  Fuzzy probabilistic approximation spaces and their information measures , 2006, IEEE Transactions on Fuzzy Systems.

[51]  Chris Cornelis,et al.  Fuzzy Rough Sets: The Forgotten Step , 2007, IEEE Transactions on Fuzzy Systems.

[52]  Ivo Diintsch.  Uncertainty measures of rough set prediction , 2003 .

[53]  Bart Baesens,et al.  A new approach for measuring rule set consistency , 2007, Data Knowl. Eng..

[54]  Wen-Xiu Zhang,et al.  Theory of including degrees and its applications to uncertainty inferences , 1996, Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium.