Learning algorithms and dimensionality

Approximation theory based on fuzzy sets provides a tool for modeling complex systems for which only an imprecise or approximate specification is available. In classical modeling, the system relationships are expressed mathematically as a function whose domain consists of the possible inputs to the system and whose range is the appropriate responses. Due to the complexity of the interactions in sophisticated systems, it has become increasingly difficult to construct mathematical models directly from one's knowledge of the system. A fuzzy model provides a functional approximation of the relationships of the underlying system defined by a set of fuzzy rules. The popularity of fuzzy models is attributable to the ability to represent relationships that are too complex or not well enough understood to be directly described by precise mathematical models. The objective of both experimental analysis and propagation application is to determine if the advantages of the two-level model that have been previously demonstrated carry over to more complex problem domains. The results and techniques presented in the paper represent preliminary investigations into the robustness of the learning algorithm in the face of increasing complexity. Ultimately, creating robust learning algorithms will require the combination of many techniques which are dependent upon both type of training data available and the basic properties of the system being modeled.