Confidence interval of fuzzy models: An example using a waste-water treatment plant

In this paper we present a new approach to fuzzy confidence interval identification. The method combines a fuzzy identification methodology with some ideas from applied statistics. The idea is to find, on a finite set of measured data, the confidence interval defined by the lower and upper fuzzy bound that define the band that contains all the output measurements. The method can be successfully used when we are trying to describe a family of uncertain nonlinear functions or when we are trying to find the interval for a nonlinear process output where all the measurements can be found. The fuzzy confidence interval model can be used in process monitoring, fault detection or in the case of robust control design. In our example the proposed method is used for waste-water treatment plant modeling, which exhibit a very nonlinear behavior.