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As shown in a recent paper, the fuzzy transform can be reinterpreted as a sampling process with an ill-known sampling kernel (or point spread function). This reinterpretation leads to an interval-valued direct fuzzy transform: the non-additive fuzzy transform. It provides the convex set of all sampled values that should have been obtained by sampling a continuous signal with a convex set of sampling...
In this note, we propose a solution to an open problem, which was presented by Mesiar and Stupňanová. We give two counterexamples to show that the hypothesis is not sufficient to get the result and we propose that the sufficient condition of the hypothesis is held by modifying the symmetry condition.
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