Belief Functions on the Real Line Defined by Transformed Gaussian Random Fuzzy Numbers

The recently introduced theory of epistemic random fuzzy sets extends both Dempster-Shafer and possibility theories, by allowing the representation of partially reliable and fuzzy evidence. Within this formalism, we study transformations of random fuzzy sets by one-to-one mappings, and show that such transformations commute with combination. We apply this result to define parameterized models of random fuzzy numbers, which generalize Gaussian random fuzzy numbers and allow us to construct easily combinable belief functions on a real interval. We apply this idea to the prediction of proportions.