SGER: Modeling Uncertainty in Engineering Design: An Investigation of Measure Theoretic Principles CharacterizingPreferences Under Imprecise Risk

该项目的探索性研究集中于开发一种不精确的风险理论，该理论与成熟的工程设计数学一致，但允许主观指定的概率度量。工程设计活动通常要求对所有不确定的设计输入进行概率度量的先验主观赋值。虽然主观的概率度量先验分配消除了风险表征的不精确性，但此类练习的经验表明，决策者不一定是自洽的，并且在尝试分配概率时往往不满足概率度量和/或效用理论的公理。这项研究活动的目标是：(1)使用测量理论原理调查与工程设计决策相关的不精确风险；(2)从基于测量的原理出发，使用主观分配的概率测量来开发风险的概率界限。如果这项研究工作被证明是成功的，它将提供一个分析框架，用于量化由于经常不一致的、主观分配的事件概率而产生的不精确风险。这将大大改善几乎所有工程设计的决策。

The exploratory research addressed by this project focuses upon development of a theory of imprecise risk that is consistent with well-established engineering design mathematics, yet allows subjectively specified probability measure. Engineering design activity often requires the a priori subjective assignment of a probability measure to all uncertain design inputs. While subjective a priori assignment of probability measure eliminates imprecision in the characterization of risk, experience with such exercises shows that decision makers are not necessarily self-consistent and often do not satisfy the axioms of probability measure and/or utility theory when attempting to assign probabilities. The objectives of this research activity are: (1) to investigate imprecise risk associated with decision making in engineering design using measure theoretic principles; (2) to develop, from measure-based principles probability bounds on risk using subjectively assigned probability measure. Should this research effort prove successful, it will provide an analytical framework for quantifying imprecise risk arising from often inconsistent, subjectively assigned event probabilities. This will enable substantially improved decision making in virtually all engineering design.