Fuzzy transform was proposed by Perfilieva in [3] to approximate real and(residuated) lattice-valued functions. For lattice-valued functions, the (directand inverse) upper and lower lattice-valued fuzzy transforms were introduced,and it was shown that compositions of direct and inverse fuzzy transformsprovide the lower and upper approximations of lattice-valued functions. In[4], there was demonstrated that the definition of the upper and lower lattice-valued fuzzy transforms can be expressed in terms of Sugeno-like integrals fortrivial fuzzy measures defined on the power sets of domains of lattice-valuedfunctions, particularly one fuzzy measure assigns zero to the empty set, andone to any non-empty subset of a given set (domain of functions)X, andthe second fuzzy measure assigns one to the setX, and zero to any subset ofXdifferent fromX. In addition, the fuzzy partition, which forms the coreof any fuzzy transform, can be replaced by a more general kernel functioncommonly used in the case of integral transforms for real or complex-valuedfunctions. This observation naturally leads to a generalization of the upperand lower lattice-valued fuzzy transforms, denoted as an integral transformfor lattice-valued functions. Basic properties of integral transform based onthree types of Sugeno-like integrals introduced in [1, 2] can be found in [4, 5],and an application to multicriteria decision making in [6].An open question for various integral transforms was whether the compo-sition of appropriate integral transforms can be used to reconstruct originallattice-valued functions in a similar way as the composition of direct andinverse lattice-valued fuzzy transforms. The talk focuses on this problemand its solution, specifically we want to present the reconstruction of theoriginal functions using the composition of integral transforms and show therelationship between the original functions and their reconstructions.