Transparent Fuzzy Modelling

Abstract

One of the objectives of machine learning is to enable intelligent systems to acquire knowledge in a highly automated manner. In systems modelling and control engineering, fuzzy systems have shown to be highly suitable for the modelling of complex and uncertain systems. Recently, the interest in fuzzy systems has shifted from the seminal ideas about modelling the process or the behaviour of operators by knowledge acquisition towards a data-driven approach. Reasons to choose fuzzy systems instead of modelling techniques such as neural networks, radial basis functions, genetic algorithms or splines, are mainly the possibility of integrating logical information processing with the attractive mathematical properties of general function approximators. Furthermore, the rule-based structure of fuzzy systems makes analysis easier. The fuzzy sets in the rules represent linguistic qualitative terms that approximate the human-like way of information quantization. However, many of the data-driven fuzzy modelling algorithms that have been developed, aim at good numerical approximation and pay little attention to the semantical properties of the resulting rule base. In this article, we briefly discuss different approaches to data-intensive fuzzy modelling reported in the literature. Next, we present a data-driven approach to fuzzy modelling that provides the user with both accurate and transparent rule bases. The method has two main steps: data exploration by means of fuzzy clustering and fuzzy set aggregation by means of similarity analysis. First, fuzzy relations are identified in the product space of the system's variables and are described by means of fuzzy production rules. Compatible fuzzy concepts defined for the individual variables are then identified and aggregated to produce generalizing concepts, giving a comprehensible rule base with increased semantic properties. The transparent fuzzy modelling approach is demonstrated on a real world problem concerning the modelling of algae growth in lakes.