The stack filter is the largest class of nonlinear digital filters, including weighted median filters and morphology filters. The design of the stack filter is reduced to the problem of determination of the Boolean function defining its filter and is divided into design methods of estimation type using a training signal, and design methods maximizing the noise elimination capability under the constraint of preserving a specific configuration. With a view to expanding the class of stack filters, the authors have proposed the fuzzy stack filter, a stack filter defined by the fuzzy Boolean function. Also, for the fuzzy weighted median filter, as the most fundamental fuzzy stack filter, a design method based on the estimation standpoint is provided. In this paper, a new fuzzy stack filter preserving a specific structure is explained. The noise elimination characteristics of the fuzzy stack filter preserving a specific structure and the preservation characteristics of the specific structure under the effect of the noise are clarified. Further, a procedure is presented for deriving a filter suitable for restoration of the degraded images in a wide range without departing from the standpoint of a design method preserving the specific structure (for which empirical information on the signal to be processed cannot be obtained). The effectiveness of the filter obtained by this procedure is presented.