The WM method completed: a flexible fuzzy system approach to data mining

In this paper, the so-called Wang-Mendel (WM) method for generating fuzzy rules from data is enhanced to make it a comprehensive and flexible fuzzy system approach to data description and prediction. In the description part, the core ideas of the WM method are used to develop three methods to extract fuzzy IF-THEN rules from data. The first method shows how to extract rules for the user-specified cases, the second method generates all the rules that can be generated directly from the data, and the third method extrapolates the rules generated by the second method over the entire domain of interest. In the prediction part, two fuzzy predictive models are constructed based on the fuzzy IF-THEN rules extracted by the methods of the description part. The first model gives a continuous output and is suitable for predicting continuous variables, and the second model gives a piecewise constant output and is suitable for predicting categorical variables. We show that by comparing the prediction accuracy of the fuzzy predictive models with different numbers of fuzzy sets covering the input variables, we can rank the importance of the input variables. We also propose an algorithm to optimize the fuzzy predictive models, and show how to use the models to solve pattern recognition problems. Throughout this paper, we use a set of real data from a steel rolling plant to demonstrate the ideas and test the models.