An optimized method to calculate approximations in Dominance based Rough Set Approach

Abstract

Classical Rough Set Theory (RST) is a prominent tool to deal with uncertainty of categorical data. However, it does not consider the preference order between the values of the attributes. Dominance Based Rough Set Approach (DRSA) provides dominance relation in this regard. Computation of the upper and lower approximation is a critical step in DRSA. However, computing these approximations is a computationally expensive task. Efficiently computing approximations will thus be helpful in reducing the execution time of algorithms using these approximations. In this paper, we have proposed an efficient approach to compute these measures. The proposed approach directly calculates approximations without considering the objects that do not play any role in the approximations. In our approach, one instance of a dataset is compared with another instance only once which avoids unnecessary comparisons. The proposed approach is compared with the conventional method using sixteen benchmark data sets from UCI. Results show that the proposed approach significantly reduces the execution time. The average reduction in the execution time was found to be almost 85%. This approach also reduces the memory consumption by 75%. The Big-O complexity is also reduced. These measures justify that the proposed approach is more effective and efficient as compared to the conventional DRSA.