An Equivalent Definition of Rough Sets
Using characteristic function of sets, this paper proposes the concept of linear mappings for the power sets of universal sets. Through this concept, we explain rough set upper approximation as a linear mapping and study the linear properties of rough sets. The relationship between the linear mappings and the upper approximations is established. The results and methods given in this paper will hopefully simplify the theoretical and practical researches of rough sets.
KeywordsRough sets Binary relations Approximations Composition of relations Characteristic functions
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- 1.Grassmann, W.K., Tremblay, J.P.: Logical and discrete mathematics, A computer science perspective. Prentice-Hall, Inc., Englewood Cliffs (1996)Google Scholar