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Article Dans Une Revue Fuzzy Sets and Systems Année : 2023

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

Résumé

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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Dates et versions

hal-03915957 , version 1 (30-12-2022)
hal-03915957 , version 2 (18-03-2023)

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Thierry Denœux. Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: General framework and practical models. Fuzzy Sets and Systems, 2023, 453, pp.1-36. ⟨10.1016/j.fss.2022.06.004⟩. ⟨hal-03915957v1⟩
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