Redefining preliminaries of dominance-based rough set approach

Classical Rough Set Theory (RST) is a prominent tool to deal with uncertainty of categorical data. However, in a case where values of attributes maintain preference order over each other, RST does not consider it. Dominance-based Rough Set Approach (DRSA), a generalization of RST, studies the dominance aspect of attributes and defines the dominance relation. The lower and upper approximations form the basis of most algorithms based on RST. However, determining DRSA approximations is computationally expensive so that the algorithms using approximations may suffer serious performance bottleneck when dealing with datasets of larger sizes. In this paper, we proposed a heuristic approach to compute lower and upper approximations based on DRSA, in time efficient manner. The proposed algorithm directly calculates approximations without going through the heavy computations of dominance positive or negative cones. We introduce heuristic rules to calculate approximations without considering the intersection and subset relations. By using the properties and logical structure of approximations, our mathematical implications select an object for all relevant approximation sets. The proposed approach was compared with the conventional method using eleven benchmark datasets from UCI. The results showed that the proposed rules significantly reduce the execution time by avoiding the redundant computations, which ultimately affect the structural complexity and memory requirements. The average reduction in execution time was found to be 83%. The proposed approach also reduces the structural complexity and memory consumption by 89.69%.