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arXiv · 2202.08081

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

Thierry Denoeux
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Abstract

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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Thierry Denoeux. 2022-02-16. Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models. https://doi.org/10.1016/j.fss.2022.06.004

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