Los Angeles, CA
March 31, 2009 to April 2, 2009
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 non-empty subsets of the vector space. Some characterizations of the approximation operators are expressed, and some counter examples are given.
Mingfen Wu, Cungen Cao, "Rough Subset Based on Congruence in a Vector Space", CSIE, 2009, 2009 WRI World Congress on Computer Science and Information Engineering, CSIE, 2009 WRI World Congress on Computer Science and Information Engineering, CSIE 2009, pp. 335-339, doi:10.1109/CSIE.2009.292