Basic Numerical Mathematics: Numerical Algebra
Basic Numerical Mathematics: Numerical Algebra
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 neural network approach to the fuzzy transform
Fuzzy Sets and Systems
Fuzzy transforms: Theory and applications
Fuzzy Sets and Systems
Transactions on Rough Sets II
B-spline signal processing. I. Theory
IEEE Transactions on Signal Processing
B-spline signal processing. II. Efficiency design and applications
IEEE Transactions on Signal Processing
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In this study, the inverse fuzzy transform recently introduced by Perfilieva is compared to a new representation of signals that we name the fuzzy projection. Both representations are sampling/interpolation schemes in a given fuzzy context. Fuzzy projection is closely related to fuzzy and inverse fuzzy transforms and is presented in this framework. We deal with these two operators in the space of finite energy signals, while proposing theoretical and numerical comparisons. After presenting convergence results for fuzzy projection, some numerical tests are performed on signals. They confirm the theoretical studies, and show the superiority of fuzzy projection for handling, in the L^2 sense, signals without too high frequencies since both representations can be regarded as low pass filtering processes. They also show the robustness of fuzzy projection with respect to noise, suggesting future studies in simultaneous compression and denoising.