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Nonlinear filters are known to be effective for restoration of image signals subject to additive noise. Among them, the most typical are median filters, and particularly popular are stack filters. Signal processing in the stack filters involves the following three stages: threshold value decomposition, calculation of the Boolean function output at each level, and signal synthesis. The Boolean function is defined by the binary input/output. However, to achieve better filter characteristics and design diversity, the authors considered using fuzzy Boolean functions defined by continuous output values from 0 to 1, rather than conventional Boolean functions. In the current study, the authors performed fuzzification of such common stack filters as the median filter and center weighted median (CWM) filter. Fuzzification was performed by using fuzzy Boolean functions to define the median filter or the CWM filter. The fuzzy Boolean function is derived from fuzzy inference. As a next step, the authors developed a method for fuzzy inference optimization (tuning method). © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(2): 83–94, 1999 [ABSTRACT FROM AUTHOR]