A comparison of smoothing filter based on fuzzy transform and Nadaraya-Watson estimators

Data smoothing is an important step within a data processing allowing one to stress the most important patterns. In literature we can find many different smoothing techniques and filter types. Recently, Holapek and Tich (2010, 2011) suggested smoothing filters based on fuzzy transform approach introduced by Perfilieva (2004). For this purpose, a generalization of the concept of fuzzy partition was suggested and the smoothing filter was defined as a combination of the direct discrete fuzzy transform and a slightly modified inverse continuous fuzzy transform. In this paper we compare the proposed filter with the Nadaraya-Watson estimator. We provide an approximative relation of both filters by an optimal parameter selection.