Prediction of uncertain structural responses using fuzzy time series

Numerical methods for the prediction of uncertain structural responses with the aid of fuzzy time series are presented. Uncertain data, uncertain measured actions, and uncertain structural responses over time are considered as time series comprised of fuzzy data. Uncertain data are described by means of a new incremental fuzzy representation, which permits a complete and accurate estimation of uncertainty. The fuzzy time series are regarded as realizations of a fuzzy random process. Methods for identification and quantification of the underlying fuzzy random process are developed. The concepts of model-free and of model-based forecasting are addressed. These concepts enable the prediction of data in the form of optimal forecasts, fuzzy forecast intervals, and fuzzy random forecasts. The algorithms are demonstrated by way of practical examples.