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2009 WRI World Congress on Computer Science and Information Engineering
Rough Subset Based on Congruence in a Vector Space
Los Angeles, California USA
March 31April 02
ISBN: 9780769535074
ASCII Text  x  
Mingfen Wu, Xiangyun Xie, Cungen Cao, "Rough Subset Based on Congruence in a Vector Space," Computer Science and Information Engineering, World Congress on, vol. 4, pp. 335339, 2009 WRI World Congress on Computer Science and Information Engineering, 2009.  
BibTex  x  
@article{ 10.1109/CSIE.2009.292, author = {Mingfen Wu and Xiangyun Xie and Cungen Cao}, title = {Rough Subset Based on Congruence in a Vector Space}, journal ={Computer Science and Information Engineering, World Congress on}, volume = {4}, year = {2009}, isbn = {9780769535074}, pages = {335339}, doi = {http://doi.ieeecomputersociety.org/10.1109/CSIE.2009.292}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  Computer Science and Information Engineering, World Congress on TI  Rough Subset Based on Congruence in a Vector Space SN  9780769535074 SP335 EP339 A1  Mingfen Wu, A1  Xiangyun Xie, A1  Cungen Cao, PY  2009 VL  4 JA  Computer Science and Information Engineering, World Congress on ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CSIE.2009.292
The rough set theory proposed by Pawlak, is a generalization of the classical set theory. Many important algebraic structures are naturally endowed with two binary operations: addition and multiplication, for example, rings, groups and modules. A vector space is an algebraic structure with a binary operation and a multiplication by a scalar. This paper concerned a relationship between rough sets and vector spaces. We considered a vector space as an universal set, and assumed that the knowledge about objects should be restricted by a subspace. First, we discussed relationships between congruences and subspaces of a vector space. Then we defined a pair of rough approximation operators based on a subspace, and obtained some properties of lower (upper) approximation of nonempty subsets of the vector space. Some characterizations of the approximation operators are expressed, and some counter examples are given.
Citation:
Mingfen Wu, Xiangyun Xie, Cungen Cao, "Rough Subset Based on Congruence in a Vector Space," csie, vol. 4, pp.335339, 2009 WRI World Congress on Computer Science and Information Engineering, 2009
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