使用认知随机模糊集推理模糊与不确定证据：通用框架与实用模型
Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models
AI总结：
提出认知随机模糊集通用理论以统一 Dempster-Shafer 理论与可能性理论，并引入 Gaussian 随机模糊数和向量作为可闭式计算的实用不确定性模型。
摘要：
我们提出了一种用于基于模糊或清晰证据进行推理的认知随机模糊集通用理论。该框架同时推广了 Dempster-Shafer 信任函数理论和可能性理论。相互独立的认知随机模糊集通过广义乘积–交并规则进行组合，该规则既扩展了用于组合信任函数的 Dempster 规则，也扩展了可能性分布的乘积合取组合。我们引入 Gaussian 随机模糊数及其多维扩展 Gaussian 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 Gaussian 随机模糊数和向量在组合、投影与空扩展方面的闭式表达式。
英文摘要：
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.
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