Intervals´ Numbers (INs) interpolation/extrapolation

An Intervals´ Number (IN) is a mathematical object known to represent either a probability distribution or a possibility distribution. The space of INs has been studied during the last years. After summarizing some instrumental mathematical results, this work demonstrates comparatively novel schemes for tunable fuzzy rule interpolation and extrapolation. Extensions to Type-2 fuzzy sets are straightforward. Finally, this work demonstrates a preliminary application, regarding the reconstruction of partially occluded human facial expressions, based on a neural network that may predict a data distribution from other ones. Far reaching extensions of the proposed techniques are discussed.