An approach to covering-based rough sets through bipartite graphs

Covering is an important form of data, and covering-based rough sets provide an effective tool to deal with this data. In this paper, we use bipartite graphs to study covering-based rough sets. Firstly, a bipartite graph is constructed through a covering, named bipartite graph associated with a covering. According to a bipartite graph associated with a covering, two equivalent representations of a pair of covering approximation operators are presented. Then, some properties of this pair of covering approximation operators and reducible elements in a covering are investigated through the constructed bipartite graph. In a word, these results show an interesting view of graphs to investigate covering-based rough sets.

[1]  James A. Mason,et al.  Discrete mathematics for computer science , 1992 .

[2]  Qinghua Hu,et al.  A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets , 2007, Inf. Sci..

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

[4]  William Zhu,et al.  Contraction to Matroidal Structure of Rough Sets , 2013, RSKT.

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

[6]  Yumin Chen,et al.  A rough set approach to feature selection based on power set tree , 2011, Knowl. Based Syst..

[7]  William Zhu,et al.  Applications of Matrices to a Matroidal Structure of Rough Sets , 2013, J. Appl. Math..

[8]  Ying Sai,et al.  Invertible approximation operators of generalized rough sets and fuzzy rough sets , 2010, Inf. Sci..

[9]  Lingping Zhong,et al.  The harmonic index for graphs , 2012, Appl. Math. Lett..

[10]  Qinghua Hu,et al.  Data compression with homomorphism in covering information systems , 2011, Int. J. Approx. Reason..

[11]  Gianpiero Cattaneo,et al.  Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems , 2007, Fundam. Informaticae.

[12]  Bijan Davvaz,et al.  Roughness based on fuzzy ideals , 2006, Inf. Sci..

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

[14]  Qingguo Li,et al.  Related family: A new method for attribute reduction of covering information systems , 2013, Inf. Sci..

[15]  Fei Li,et al.  Approaches to knowledge reduction of covering decision systems based on information theory , 2009, Inf. Sci..

[16]  N. D. Thuan,et al.  Covering Rough Sets From a Topological Point of View , 2012, ArXiv.

[17]  Meng Guang-wu.  LF-topological methods on the theory of covering generalized rough sets , 2008 .

[18]  Wei-Zhi Wu,et al.  On axiomatic characterizations of three pairs of covering based approximation operators , 2010, Inf. Sci..

[19]  William Zhu,et al.  Matroidal structure of covering-based rough sets through the upper approximation number , 2011, Int. J. Granul. Comput. Rough Sets Intell. Syst..

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

[21]  William Zhu,et al.  Bipartite Graphs and Coverings , 2011, RSKT.

[22]  Sankar K. Pal,et al.  Rough-Fuzzy MLP: Modular Evolution, Rule Generation, and Evaluation , 2003, IEEE Trans. Knowl. Data Eng..

[23]  Andrzej Skowron,et al.  Modeling rough granular computing based on approximation spaces , 2012, Inf. Sci..

[24]  Guilong Liu,et al.  The relationship among different covering approximations , 2013, Inf. Sci..

[25]  Ping Zhu,et al.  An Axiomatic Approach to the Roughness Measure of Rough Sets , 2009, Fundam. Informaticae.

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

[27]  William Zhu,et al.  Covering-Based Rough Sets on Eulerian Matroids , 2013, J. Appl. Math..

[28]  Gianpiero Cattaneo,et al.  Entropies and Co-entropies for Incomplete Information Systems , 2007, RSKT.

[29]  Michiro Kondo,et al.  On the structure of generalized rough sets , 2006, Inf. Sci..

[30]  Wei-Zhi Wu,et al.  Covering-Based Generalized Rough Fuzzy Sets , 2006, RSKT.

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

[32]  Qingguo Li,et al.  Reduction about approximation spaces of covering generalized rough sets , 2010, Int. J. Approx. Reason..

[33]  William Zhu,et al.  Relationship among basic concepts in covering-based rough sets , 2009, Inf. Sci..

[34]  Francesc Rosselló,et al.  On the coverings by tolerance classes , 2004, Inf. Sci..

[35]  Yiyu Yao,et al.  Covering based rough set approximations , 2012, Inf. Sci..

[36]  Qinghua Hu,et al.  Neighborhood rough set based heterogeneous feature subset selection , 2008, Inf. Sci..

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

[38]  Fei-Yue Wang,et al.  Conditions for coverings to induce matroids , 2014, Int. J. Mach. Learn. Cybern..

[39]  Qinghua Hu,et al.  Rule learning for classification based on neighborhood covering reduction , 2011, Inf. Sci..

[40]  William Zhu,et al.  Transversal and Function Matroidal Structures of Covering-Based Rough Sets , 2011, RSKT.

[41]  D. West.  Introduction to Graph Theory , 1995 .