This article proposes a new interval-valued fuzzy transform. Its construction is based on a possibilistic interpretation of the partition on which the fuzzy transform is built. The main advantage of this approach is that it provides specific interval valued functions whose interpretation is straightforward. This interpretation relates to a traditional sampling/reconstruction framework where little is known about the sampling and/or reconstructing kernels. Numerous properties of the proposed approach are proved that could be useful for function analysis and comparison. In the experimental section, we illustrate some properties of the proposed transform while highlighting interesting features of the obtained framework.