Construction of Fuzzy Systems - Interplay between Precision and Transparency

In recent years, we have witnessed a strong emphasis on high performance and precision of fuzzy systems. Many publications are focused on data driven approaches, i.e., the construction of fuzzy systems from data and applying them in areas like data mining, pattern recognition, prediction or control. In such applications, fuzzy system inevitably must be compared with other inductive methods, like neural networks, machine learning or statistical techniques. The most prominent feature that distinguishes fuzzy systems from many other techniques is their transparency and interpretability. Fuzzy models are ideally suited for explaining solutions to users. In the current literature, however, surprisingly little attention has been devoted to the study of the interplay between interpretability and precision. These objectives are to a certain degree conflicting and attention must be paid to both of them. In this paper, the interpretation and transparency issues are first discussed with regard to the various parameters (degrees of freedom) in the Mamdani and Takagi--Sugeno models. An overview is also given of methods for improving the transparency and interpretability of fuzzy systems induced from data. These include the use of similarity measures, semantic constraints and multi-objective optimization.