This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak complementation denoted as $\psi$. The interval probability measure of an event $H$ is defined with respect to the set of indecisive eventualities $(\psi(H))^c$, which is included in the standard complement $H^c$. We characterize a broad class of interval probability measures and define their properties. Additionally, we establish an updating rule with respect to $H$, incorporating concepts of statistical independence and dependence. The interval distribution of a random variable is formulated, and a corresponding definition of stochastic dominance between two random variables is introduced. As a byproduct, a formal solution to the century-old Keynes-Ramsey controversy is presented.

翻译：本文提出了一种区间概率测度的新概念，能够以自然且连贯的方式表示不精确概率或不确定性。在集合代数框架内，我们引入了弱互补性概念，记作$\psi$。事件$H$的区间概率测度是相对于一组不确定事件$(\psi(H))^c$定义的，该集合包含于标准补集$H^c$中。我们刻画了一类广泛的区间概率测度，并定义了其性质。此外，我们建立了基于$H$的更新规则，并融入了统计独立性与依赖性的概念。本文还给出了随机变量的区间分布，并引入了两个随机变量之间随机优势的相应定义。作为副产品，我们为存在已久的凯恩斯-拉姆齐争议提供了形式化解决方案。