Interval fuzzy model identification using l∞-norm

In this paper, we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. We consider a finite set of measured data, and we use an optimality criterion that minimizes the maximum estimation error between the data and the proposed fuzzy model output. The idea is then extended to modeling the optimal lower and upper bound functions that define the band which contains all the measurement values. This results in lower and upper fuzzy models or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). We also showed that the proposed structure uniformly approximates the band of any nonlinear function. The interval fuzzy model identification is a methodology to approximate functions by taking into account a finite set of input and output measurements. This approach can also be used to compress information in the case of large amount of data and in the case of robust system identification. The method can be efficiently used in the case of the approximation of the nonlinear functions family. If the family is defined by a band containing the whole measurement set, the interval of parameters is obtained as the result. This is of great importance in the case of nonlinear circuits' modeling, especially when the parameters of the circuits vary within certain tolerance bands.