Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Weighted fuzzy mean filters for image processing
Fuzzy Sets and Systems
Nonparametric econometrics
Fuzzy Filters for Image Processing
Fuzzy Filters for Image Processing
Fuzzy transform in the analysis of data
International Journal of Approximate Reasoning
An image coding/decoding method based on direct and inverse fuzzy transforms
International Journal of Approximate Reasoning
A segmentation method for images compressed by fuzzy transforms
Fuzzy Sets and Systems
Fuzzy transforms method and attribute dependency in data analysis
Information Sciences: an International Journal
Fuzzy transforms: Theory and applications
Fuzzy Sets and Systems
Fuzzy transform as an additive normal form
Fuzzy Sets and Systems
Transactions on Rough Sets II
Fuzzy transforms and their applications to image compression
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
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This paper is devoted to the smoothing of discrete functions using the fuzzy transform introduced by Perfilieva. We generalize a smoothing filter based on the fuzzy transform recently proposed by us to obtain a better control on the smoothed functions. For this purpose, a generalization of the concept of fuzzy partition is suggested and the smoothing filter is defined as a combination of the direct discrete fuzzy transform and a slightly modified inverse continuous fuzzy transform. An approximation behavior, total variation of smoothed functions and statistical properties including the description of the white noise reduction and the asymptotic expression of bias and variance are investigated and discussed. The proposed filter is compared with the Nadaraya-Watson estimator and the results are illustrated assuming financial data.