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

翻译：本文提出了一种基于认知随机模糊集的一般性理论，用于处理模糊或清晰证据的推理。该框架既推广了Dempster-Shafer信度函数理论，又推广了可能性理论。通过广义乘积-交集规则实现独立认知随机模糊集的组合，该规则同时拓展了用于组合信度函数的Dempster规则和可能性分布的乘积合取组合方法。我们引入高斯随机模糊数及其多维扩展形式——高斯随机模糊向量，作为量化标量或向量量不确定性的实用模型，并推导了这些模型在组合、投影和空化扩展中的闭式表达式。