A min-max approach to fuzzy clustering, estimation, and identification

This study, for any unknown physical process y=f(x₁,...,x_n), is concerned with the: 1) fuzzy partition of n-dimensional input space X=X₁timesmiddotmiddotmiddottimesX_n into K different clusters, 2) estimating the process behavior ycirc=f(xcirc) for a given input xcirc=(xcirc₁,middotmiddotmiddot,xcirc_n )isinX, and 3) fuzzy approximation of the process, with uncertain input-output identification data {(x(k)plusmndeltax_k ),(y(k)plusmnv_k)}_k=1,..., using a Sugeno type fuzzy inference system. A unified min-max approach (that attempts to minimize the worst-case effect of data uncertainties and modeling errors on estimation performance), is suggested to provide robustness against data uncertainties and modeling errors. The proposed method of min-max fuzzy parameters estimation does not make any assumption and does not require a priori knowledge of upper bounds, statistics, and distribution of data uncertainties and modeling errors. To show the feasibility of the approach, simulation studies and a real-world application of physical fitness classification based on the fuzzy interpretation of physiological parameters, have been provided