Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models
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.
Cite
@article{arxiv.2202.08081,
title = {Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models},
author = {Thierry Denoeux},
journal= {arXiv preprint arXiv:2202.08081},
year = {2024}
}