In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we introduced the concepts of weak complementation and interval probability measures associated with a family of random variables, which effectively capture the inherent uncertainty in any event. This paper conducts a comprehensive analysis of these concepts within a specific probability space. Additionally, we elaborate on an updating rule for events, integrating essential concepts of statistical independence, dependence, and stochastic dominance.

翻译：在Basili和Pratelli（2024）的研究中，引入了一种新颖且自洽的区间概率测度概念，为表示不精确概率和不确定性提供了方法。在集合代数框架下，我们引入了弱互补性概念以及与一族随机变量相关的区间概率测度，这些概念有效捕捉了任何事件中固有的不确定性。本文在特定概率空间内对这些概念进行了全面分析。此外，我们详细阐述了事件的更新规则，整合了统计独立性、依赖性和随机优势等基本概念。