Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models
This provides a unified mathematical framework for handling uncertainty in AI and decision-making systems, though it appears to be an incremental extension of existing theories.
The authors tackled the problem of reasoning with fuzzy and uncertain evidence by introducing a general framework of epistemic random fuzzy sets, which unifies and extends Dempster-Shafer theory and possibility theory, and developed practical Gaussian-based models with closed-form expressions for operations like combination and projection.
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.