A PRACTICAL APPROACH TO NONLINEAR FUZZY REGRESSION

This paper presents a new method of mathematical modeling in an uncertain environment. The uncertainties of data and model are treated using concepts of fuzzy set theory. The model fitting principle is the minimization of a least squares objective function. A practical modeling procedure is obtained by restricting the type of data and parameter fuzziness to conical membership functions. Under this restriction, the model fitting problem can be solved numerically with the aid of any least squares software for regression with implicit constraint equations. The paper contains a short discussion of the geometry of fuzzy point and function spaces with conical membership functions, and illustrates the application of fuzzy regression with an example from terminal ballistics.