Random set system identification
The first part of this paper is 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. In the second section, 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. In the second part of the paper, the technique is adapted to nonlinear time series analysis. A practical application of a nonlinear dynamic plant is presented in the third part.
random set coverage function possibility measure fuzzy set model quality multivalued mapping multivalued statistics probability theory random sets sample random variable time-series analysis