Experiments on probabilistic approximations

Recently much attention has been paid to probabilistic (parameterized) approximations that are generalizations of ordinary lower and upper approximations known from rough set theory. The first objective of this paper is to compare the quality of such approximations and ordinary, lower and upper approximations. The second objective is to show that the number of distinct probabilistic approximations is quite limited. In our experiments we used six real-life data sets. Obviously, inconsistent data sets are required for such experiments, so the level of consistency in all data sets used for our experiments was decreased to enhance our experiments. Our main result is rather pessimistic: probabilistic approximations, different from ordinary lower or upper approximations, were better than ordinary approximations for only two out of these six data sets.