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

本项目的探索性研究侧重于不精确风险理论的发展，该理论与成熟的工程设计数学相一致，但允许主观指定的概率测量。工程设计活动通常需要对所有不确定的设计输入进行先验的主观概率分配。虽然主观先验的概率度量分配消除了风险表征中的不精确性，但此类练习的经验表明，决策者不一定是自一致的，并且在试图分配概率时往往不满足概率度量和/或效用理论的公理。本研究活动的目的是：(1)利用测量理论原理研究工程设计决策中的不精确风险；(2)从基于度量的原则出发，利用主观分配的概率度量来发展风险的概率界限。如果这项研究成功，它将提供一个分析框架，用于量化经常不一致的、主观分配的事件概率所产生的不精确风险。这将大大提高几乎所有工程设计的决策能力。

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.