Random set system identification

Abstract

The paper gives a brief review of the basic mathematical aspects of random set theory. Concepts such as a random set mapping and its coverage function are introduced in a comprehensive way, avoiding too much detail. We adapt this theory to system identification and forecasting of time series. This is achieved by using the one-point coverage function of a random set as a possibility measure of the process which generates such a time series. The coverage function of a random set defines a fuzzy set, and we thereby establish the relationship between statistical objects and fuzzy systems. The possibility measure obtained in this way can be used for either prediction or to evaluate the quality of a model with respect to the training data. The technique is adapted to nonlinear time series analysis. A practical application of a nonlinear dynamic plant is presented.