Fast Algorithm of Attribute Reduction Based on the Complementation of Boolean Function

In this chapter we propose a new method of solving the attribute reduction problem. Our method is different to the classical approach using the so-called discernibility function and its CNF into DNF transformation. We have proved that the problem is equivalent to very efficient unate complementation algorithm. That is why we propose new algorithm based on recursive execution of the procedure, which at every step of recursion selects the splitting variable and then calculates the cofactors with respect to the selected variables (Shannon expansion procedure). The recursion continues until at each leaf of the recursion tree the easily computable rules for complement process can be applied. The recursion process creates a binary tree so that the final result is obtained merging the results in the subtrees. The final matrix represents all the minimal reducts of a decision table or all the minimal dependence sets of input variables, respectively. According to the results of computer tests, better results can be achieved by application of our method in combination with the classical method.