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

• URL: http://arxiv.org/abs/2202.08081v4
• Date: Tue, 7 May 2024 08:38:27 GMT
• Title: Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models
• Authors: Thierry Denoeux,
• Abstract summary: This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. We introduce Gaussian random fuzzy numbers and their multi-dimensional extensions, Gaussian random fuzzy vectors, as practical models for quantifying uncertainty.
• Score: 4.6684925321613076
• License: http://creativecommons.org/licenses/by/4.0/
• 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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