Finding all the absolute reductions based on discernibility matrix

Rough-set-based-method to simplify a decision table is of great importance. We can calculate the absolute reductions and relative reductions and core through the discernibility matrix, but the numeration is very complex and the archival memory is very large. In this paper, we present a new notion for finding all the absolute reductions in a given information system. Firstly we present the conception of an indiscernibility matrix based on discernibility matrix, secondly, through the analysis of the discernibility matrix and indiscernibility matrix and the indiscernible equivalent relation induced by attributes sets in the context of rough sets, we present two new algorithm for finding all the absolute reductions in a given information system. The new algorithms are valid to finding all the relative reductions also. In the new algorithm 1, through the Boer function analysis to the discernibility function, we can remove the elements that are independent of the calculation in the discernibility matrix. Furthermore, we can obtain the indiscernibility matrix based on discernibility matrix and place items in that in accordance with the order of the exponent, this can simplify the calculation. Consequently the numeration can be decreased. In the new algorithm 2, its complexity is the n power once of 2; it is valid to the information that consists of few attributes. Both the theoretical analysis and experimental results are made to validate to the presented new algorithm.