效用三支决策模型

摘要

Risk decisions are usually influenced by subjective and objective factors. During the process of decision⁃making, decisions are based not only on the objective risk but also on the subjective activity of decision⁃makers. In order to introduce decision⁃makers’ subjective attitudes to risk, a model of utility⁃based three⁃way decisions ( UT⁃WD) was produced by extending the risk function to a utility function. The monotonic relationships between the u⁃tility and probabilities of objects in three regions were investigated systematically. The computational methods for positive region utility, boundary region utility, and negative region utility are also given. Finally, an example is giv⁃en to substantiate the conceptual arguments. The model is an extension of three⁃way decisions and provides a benefi⁃cial investigation into subjective risk measures in three⁃way decision research.%风险型决策通常受主观和客观两方面因素影响，决策过程中不仅需要遵从客观存在的风险信息，而且需要发挥决策者的主观能动性。为了在决策过程中引入决策者对于风险的主观态度，本文把效用理论应用于三支决策模型，通过将风险损失函数扩展为效用函数提出了基于效用的三支决策模型。研究了效用与对象的概率之间的单调关系，给出了效用三支决策中正域效用、边界域效用与负域效用的计算方法。最后，通过算例对提出的效用三支决策模型进行了有效地分析。该模型是经典三支决策模型的扩展，为三支决策模型中风险的主观量化研究提供了有益探索。