Rule Induction from Numerical Data Based on Rough Sets Theory

To induce rules from numerical data by rough sets, there are two kinds of methods. One is to discretize the original data and then apply the crisp rough sets models. Here the rough sets models which can only deal with the nominal data are called crisp rough sets models. The other is to fuzzify the original data and then apply fuzzy rough sets models. There are some problems on both of these methods on rules induction such as information loss after discretization or increasing of data size after fuzzification. In this paper we make an attempt to propose one method to induce rules without discretization or fuzzification. Firstly the indiscernibility relation which is the underlining concept of rough sets is redefined as the similarity relation. Subsequently, the concepts of knowledge reduction are proposed based on the similarity relation. Finally, the numerical experiments show that our method is feasible and effective