A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets

Efficient attribute reduction in large, incomplete decision systems is a challenging problem; existing approaches have time complexities no less than O(|C|^2|U|^2). This paper derives some important properties of incomplete information systems, then constructs a positive region-based algorithm to solve the attribute reduction problem with a time complexity no more than O(|C|^2|U|log|U|). Furthermore, our approach does not change the size of the original incomplete system. Numerical experiments show that the proposed approach is indeed efficient, and therefore of practical value to many real-world problems. The proposed algorithm can be applied to both consistent and inconsistent incomplete decision systems.

[1]  Zhongzhi Shi,et al.  Rough Set Based Image Texture Recognition Algorithm , 2004, KES.

[2]  Wei-Zhi Wu,et al.  Approaches to knowledge reductions in inconsistent systems , 2003, Int. J. Intell. Syst..

[3]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

[4]  Shusaku Tsumoto,et al.  Mining diagnostic rules from clinical databases using rough sets and medical diagnostic model , 2004, Inf. Sci..

[5]  Urszula Wybraniec-Skardowska,et al.  Extensions and Intentions in the Ruogh Set Theory , 1998, Inf. Sci..

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

[7]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

[8]  S. Pal,et al.  Rough-Fuzzy C-Medoids Algorithm and Selection of Bio-Basis for Amino Acid Sequence Analysis , 2007, IEEE Transactions on Knowledge and Data Engineering.

[9]  Daniel S. Yeung,et al.  Rough approximations on a complete completely distributive lattice with applications to generalized rough sets , 2006, Inf. Sci..

[10]  Zhongzhi Shi,et al.  Tolerance Relation Based Granular Space , 2005, RSFDGrC.

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

[12]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[13]  William Zhu,et al.  Topological approaches to covering rough sets , 2007, Inf. Sci..

[14]  Chen Degang,et al.  A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets , 2007 .

[15]  Yee Leung,et al.  Maximal consistent block technique for rule acquisition in incomplete information systems , 2003, Inf. Sci..

[16]  Daniel Vanderpooten,et al.  A Generalized Definition of Rough Approximations Based on Similarity , 2000, IEEE Trans. Knowl. Data Eng..

[17]  Marzena Kryszkiewicz.  Comparative study of alternative types of knowledge reduction in inconsistent systems , 2001, Int. J. Intell. Syst..

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

[19]  David Soldani.  Means and methods for collecting and analyzing QoE measurements in wireless networks , 2006, 2006 International Symposium on a World of Wireless, Mobile and Multimedia Networks(WoWMoM'06).

[20]  Yee Leung,et al.  A rough set approach to the discovery of classification rules in spatial data , 2007, Int. J. Geogr. Inf. Sci..

[21]  Yiyu Yao,et al.  Potential Applications of Granular Computing in Knowledge Discovery and Data Mining , 2008 .

[22]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[23]  Qinghua Hu,et al.  Neighborhood classifiers , 2008, Expert Syst. Appl..

[24]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[25]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

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

[27]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[28]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

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

[30]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

[31]  Yiyu Yao,et al.  Data mining using extensions of the rough set model , 1998, KDD 1998.

[32]  Qinghua Hu,et al.  Mixed feature selection based on granulation and approximation , 2008, Knowl. Based Syst..