On rough approximations of groups

It is one of useful methods for research of group theory to construct a new group by using known groups. Lower and upper approximation operators of rough sets are applied into group theory and so the notion of rough group has been introduced. In this paper, we further study the properties of rough groups and examine relationships between subgroups and their rough approximations and relationships between a normal series of a group and its rough approximations.

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

[2]  T. Y. Lin,et al.  Neighborhood systems and relational databases , 1988, CSC '88.

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

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

[5]  Anna Maria Radzikowska,et al.  A comparative study of fuzzy rough sets , 2002, Fuzzy Sets Syst..

[6]  Wei-Zhi Wu,et al.  Generalized fuzzy rough sets , 2003, Inf. Sci..

[7]  Salvatore Greco,et al.  Rough sets methodology for sorting problems in presence of multiple attributes and criteria , 2002, Eur. J. Oper. Res..

[8]  Wen-Xiu Zhang,et al.  The Lower and Upper Approximations of Fuzzy Sets in a Fuzzy Group , 2002, AFSS.

[9]  Qinghua Hu,et al.  Information-preserving hybrid data reduction based on fuzzy-rough techniques , 2006, Pattern Recognit. Lett..

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

[11]  Congxin Wu,et al.  Membership evaluation and feature selection for fuzzy support vector machine based on fuzzy rough sets , 2011, Soft Comput..

[12]  Helmut Thiele,et al.  On axiomatic characterisations of crisp approximation operators , 2000, Inf. Sci..

[13]  Bijan Davvaz,et al.  Roughness in modules , 2006, Inf. Sci..

[14]  Nehad N. Morsi,et al.  Axiomatics for fuzzy rough sets , 1998, Fuzzy Sets Syst..

[15]  Wei-Zhi Wu,et al.  Constructive and axiomatic approaches of fuzzy approximation operators , 2004, Inf. Sci..

[16]  Jun-Hai Zhai,et al.  Fuzzy decision tree based on fuzzy-rough technique , 2011, Soft Comput..

[17]  Bijan Davvaz,et al.  On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings , 2008, Inf. Sci..

[18]  Congxin Wu,et al.  Separating theorem of samples in Banach space for support vector machine learning , 2011, Int. J. Mach. Learn. Cybern..

[19]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

[20]  Jiye Liang,et al.  Positive Approximation and Rule Extracting in Incomplete Information Systems , 2007 .

[21]  Nobuaki Kuroki,et al.  Rough Ideals in Semigroups , 1997, Inf. Sci..

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

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

[24]  Degang Chen,et al.  A short note on some properties of rough groups , 2010, Comput. Math. Appl..

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

[26]  Wei-Zhi Wu,et al.  Neighborhood operator systems and approximations , 2002, Inf. Sci..

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

[28]  Jing-Yu Yang,et al.  On multigranulation rough sets in incomplete information system , 2011, International Journal of Machine Learning and Cybernetics.

[29]  Xizhao Wang,et al.  Attributes Reduction Using Fuzzy Rough Sets , 2008, IEEE Transactions on Fuzzy Systems.

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

[31]  Xizhao Wang,et al.  On the generalization of fuzzy rough sets , 2005, IEEE Transactions on Fuzzy Systems.

[32]  Yee Leung,et al.  Generalized fuzzy rough sets determined by a triangular norm , 2008, Inf. Sci..

[33]  Degang Chen,et al.  A systematic study on attribute reduction with rough sets based on general binary relations , 2008, Inf. Sci..

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

[35]  Wen-Xiu Zhang,et al.  An axiomatic characterization of a fuzzy generalization of rough sets , 2004, Inf. Sci..