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

This study, for any unknown physical process y = f (x(1), ..., x(n)), is concerned with the: 1) fuzzy partition of n-dimensional input space X = X-1 x ... x(n) into K different clusters, 2) estimating the process behavior (y) over cap = f ((x) over cap) for a given input (x) over cap = ((x) over cap (1), ... , (x) over cap (n)) is an element of X, and 3) fuzzy approximation of the process, with uncertain input-output identification data {(x(k) +/- delta x(k)), (y(k) +/- v(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.