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.

I. Introduction

Description and prediction are the two major tasks in data mining [6]. The two most commonly used data mining algorithms are decision trees [2], [11] and neural networks [12]. In fact, most commercial data mining products on the market use these two methods to construct their predictive models [8]. Decision trees and neural networks have their advantages and disadvantages. Decision trees are easy to understand and suitable for descriptive tasks, but the prediction accuracy is low due to the piecewise constant nature of the model. Neural networks give accurate prediction, but the resulting models are difficult to interpret. The fuzzy system models in this paper give accurate prediction and at the same time are easy to explain to nonspecialists. This combined description and prediction capability is achieved through the rule-based structure of the fuzzy system models. On one hand, fuzzy if–then rules are among the most convenient frameworks for humans to understand; on the other hand, by using fuzzy logic principles to combine the fuzzy if–then rules, we can construct fuzzy system predictive models that give high prediction accuracy.