Boolean Covering Approximation Space and Its Reduction

In this paper, Boolean vector algebra theory is introduced into rough set theory. A theoretical framework of Boolean covering approximation space is proposed, and based on the principle of traditional covering rough set theory, a pair of lower and upper approximation operators on a Boolean covering approximation space are defined. Properties of the lower and upper approximation operators are investigated in detail. The duality of the lower and upper approximation operators, and lower and upper definable Boolean vectors are discussed. Finally, reductions of lower and upper approximation operators are explored.

[1]  Yee Leung,et al.  Generalized fuzzy rough approximation operators based on fuzzy coverings , 2008, Int. J. Approx. Reason..

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

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

[4]  Fei-Yue Wang,et al.  Properties of the Fourth Type of Covering-Based Rough Sets , 2006, 2006 Sixth International Conference on Hybrid Intelligent Systems (HIS'06).

[5]  Daniel S. Yeung,et al.  Approximations and reducts with covering generalized rough sets , 2008, Comput. Math. Appl..

[6]  Jiye Liang,et al.  Multigranulation rough sets: From partition to covering , 2013, Inf. Sci..

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

[8]  Yiyu Yao,et al.  Probabilistic rough set approximations , 2008, Int. J. Approx. Reason..

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

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

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

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

[13]  Yiyu Yao,et al.  The superiority of three-way decisions in probabilistic rough set models , 2011, Inf. Sci..

[14]  Jing-Yu Yang,et al.  Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system , 2012, Inf. Sci..

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

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

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

[18]  Witold Pedrycz,et al.  Selecting Discrete and Continuous Features Based on Neighborhood Decision Error Minimization , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Ki Hang Kim.  Boolean matrix theory and applications , 1982 .

[20]  Guilong Liu,et al.  Rough set theory based on two universal sets and its applications , 2010, Knowl. Based Syst..

[21]  William Zhu,et al.  Relationship between generalized rough sets based on binary relation and covering , 2009, Inf. Sci..