Matrix Method for Computing Approximations in Variable Consistency Dominance-Based Rough Set Approach

Lower and upper approximations of upward (downward) union of decision classes in Variable Consistency Dominance-Based Rough Set Approach (VC-DRSA) are the basis for extraction of decision rules, so computations of approximations is a necessary step in knowledge representing and reduction based on VCDRSA. In this paper, a matrix-based method for computing lower approximations of upward and downward union of decision classes at consistency lever lis proposed. Firstly, concepts such as dominance relation matrix, consistency level, Boolean column vector of subset and the comparison operator between matrices are introduced, then a new method for computing approximations in VC-DRSA is given from matrix perspective and its correctness are proved theoretically. Furthermore, the corresponding algorithms are put forward. Finally, the matrix-based algorithms are applied to the calculation of approximations on UCI datasets and its results are compared with a previous non-matrix algorithm. The experimental results demonstrate the feasibility, conciseness and validity of the proposed matrix-based method.