Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a fuzzy prediction set \emph{is} an e-value, capturing precisely what e-values bring to predictive inference. Fuzzy prediction sets inherit the merging properties of their e-value, offer richer guarantees to decision-makers. We also show in what sense optimal e-values give rise to optimal (fuzzy) prediction sets. We apply our results to conformal prediction, deriving optimal fuzzy conformal prediction sets, and characterizing in what sense classical conformal prediction is optimal.

翻译：预测集在固定置信水平下为每个元素提供二元的包含/排除决策。我们将其推广至模糊预测集，使元素可在其自身数据驱动的置信水平下被排除。核心洞见在于：一个模糊预测集本质上就是一个e值，精准捕捉了e值对预测推断的贡献。模糊预测集继承了e值的合并特性，为决策者提供了更丰富的保证。我们还证明了在何种意义上最优e值会产生最优（模糊）预测集。我们将结果应用于共形预测，推导出最优模糊共形预测集，并刻画了经典共形预测在何种意义上具有最优性。