Fuzzy projection versus inverse fuzzy transform as sampling/interpolation schemes

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 L2 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.