The Fuzzy-ROSA Method: A Statistically Motivated Fuzzy Approach for Data-Based Generation of Small Interpretable Rule Bases in High-Dimensional Search Spaces

Abstract

In the field of data mining, fuzzy approaches are predominantly applied, if interpretable results are desired. The applicability of different methods for data-based rule generation has been demonstrated impressively in numerous real-world tasks. However, there are still difficulties in generating small interpretable rule bases efficiently, especially for applications with many input variables. The Fuzzy-ROSA method presented here was developed to overcome these problems. With the aim of reducing the computational effort for rule generation, the basic concept of the Fuzzy-ROSA method is to test and rate individual rules according to their ability to describe a relevant aspect of the system under consideration, instead of evaluating and optimizing complete rule bases. The rule base generation process is divided into the following main steps: data pre-processing for search space structuring, rule search based on rule test and rating, on- and offline rule reduction and finally rule base analysis and optimization. With respect to the broad spectrum of applications, there are different methods available for each of these steps. An overview is given in the first part of this paper, with emphasis on the rule search and rule test and rating strategies, because they are essential for the efficiency of rule generation and model quality, respectively. In the second part of the paper, the performance of the Fuzzy-ROSA method is compared with other fuzzy modeling approaches by means of benchmark problems. Moreover, we consider real-world applications: the classification of automatic gearboxes by 149 characteristics, the prediction of the duration of insurance contracts and the parameter adaptation of a position controller in robotics. It turns out that the Fuzzy -ROSA method can deal with very large search spaces, with noisy and contradictory data and that it is possible to learn from examples with different performance or quality.