On multidimensional linear modelling including real uncertainty

Abstract

The theoretical background for abstract formalization of vague phenomenon of complex systems is fuzzy set theory. In the paper are defined vague data as specialized fuzzy sets - fuzzy numbers and there is described a fuzzy linear regression model as a fuzzy function with fuzzy numbers as vague regression parameters. To identify the fuzzy coefficients of model the genetic algorithm is used. The linear approximation of vague function together with its possibility area are analytically and graphically expressed. The suitable numerical experiments are performed namely in the task of two-dimensional fuzzy function modelling and the time series fuzzy regression analysis as well.