Some Problems In The Rough Set Theory

The Rough Set Theory (RST), which was introduced by Z. Pawlak in 1982, is a tool to deal with vagueness and uncertainty. Its main idea is inducing decision or classification rule through knowledge reduction by keeping the classify ability. The main difference between the RST and other theories is that the RST does not need any preliminary information about data, so it's more objective in describing and dealing with vagueness and uncertainty.In this paper, firstly we compare RST with Fuzzy Sets Theory and introduce fuzzy method into the study of RST by the rough membership function. The exact express of the intersection and union of the fuzzy sets defined by the rough membership function is given. Two extension model of RST are introduced and their characters are discussed. We also discover the changes of the upper (lower) approximation after the attributes were added to or removed from the original attribution set.Secondly, we get two new reduction algorithms. The heuristic reduction algorithm based on the relative significance in information system is more natural and easier in computation and improves the reduction algorithm in speed. The conversional algorithm of the decision table based on the lower approximation reduction theory translate the relative reduction of the decision table into the reduction of the information system and offer a new method to find relative reduction of the decision table.At last, several measurements of roughness and their relations are discussed.