Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: General framework and practical models

We introduce a general theory of epistemic random fuzzy sets for reasoning with or crisp evidence. This framework generalizes both the Dempster-Shafer belief functions, and possibility theory. Independent are combined by generalized product-intersection rule, which extends Dempster's rule combining product conjunctive combination distributions. Gaussian numbers their multi-dimensional extensions, vectors, as practical models quantifying uncertainty about scalar vector quantities. Closed-form expressions combination, projection vacuous extension vectors derived.