We introduce an evidential model for time-to-event prediction with censored
data. In this model, uncertainty on event time is quantified by Gaussian random
fuzzy numbers, a newly introduced family of random fuzzy subsets of the real
line with associated belief functions, generalizing both Gaussian random
variables and Gaussian possibility distributions. Our approach makes minimal
assumptions about the underlying time-to-event distribution. The model is fit
by minimizing a generalized negative log-likelihood function that accounts for
both normal and censored data. Comparative experiments on two real-world
datasets demonstrate the very good performance of our model as compared to the
state-of-the-art.

我们引入了一种基于证据的模型，用于预测具有被审查数据的事件发生时间。该模型使用高斯随机模糊数量来量化事件时间的不确定性，这是一种新引入的与信任函数相关的实数随机模糊子集族，可以推广高斯随机变量和高斯可能性分布。我们的方法对于底层事件发生时间分布做出了最小化的假设。通过最小化同时考虑正常和被审查数据的广义负对数似然函数，我们对模型进行了拟合。对两个真实世界数据集进行的比较实验证明了我们模型相对于现有技术的非常好的性能。

基于高斯随机模糊数的证据时间事件预测模型

An evidential time-to-event prediction model based on Gaussian random  fuzzy numbers

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.

本文提出了一种关于认知随机模糊集的普遍理论，用于处理模糊或清晰证据，并通过广义的乘积交集规则进行独立认知随机模糊集的组合，提出了用于量化标量或矢量量，即高斯随机模糊数和多维高斯随机模糊向量的实用模型，并为组合、投影和平凡扩展推导了高斯随机模糊数和向量的公式。