Integral transform; fuzzy transform; lattice-valued functions; fuzzy kernel relation

Fuzzy transforms provide a powerful tool for reconstructing functions from compressed values called the components of fuzzy transform. Lower and upper fuzzy transforms were introduced for residuated lattice-valued functions, and it has been shown that their composition results in either upper or lower approximation of the original function depending on the order of the types of fuzzy transforms in the composition. Currently, a generalization of lower and upper fuzzy transforms was proposed using Sugeno-like integrals and fuzzy kernel relations imitating the standard integral transforms as Fourier or Laplace transforms. The paper presents preliminary results showing that a composition of two integral transforms can approximate an original function similarly as in the case of fuzzy transforms. In addition, we demonstrate that reconstruction based on integral transformations can filter outliers in a lattice-valued function.