Undefined; Missing data; Error propagation; Fuzzytransform; Image processing.

We will introduce various extensions of ordinary binary operations to a specially chosen single dummy element representing an undefined or missing value. We will apply these extensions to the Perfilieva’s fuzzy transform technique and extend it appropriately to operate with this dummy element too. The result of this extension will be called partial fuzzy transform. Moreover, we will demonstrate an usefulness of our approach using partial fuzzy transform technique on an image reconstruction problem.