Abstract: This paper proposes a method for the risky multiple attribute decision making problem considering the decision maker's partial attribute aspirations. First, according to the attribute aspiration information with regard to each nature state given by the decision maker, the original decision problem is converted into the two independent risky multiple attribute decision problems, i.e. the risky multiple attribute decision problem without attribute aspirations and the risky multiple decision problem with attribute aspirations. Then, for the risky multiple attribute decision problem without attribute aspirations, the utility value of each attribute value is calculated according to the expected utility theory, and the comprehensive utility value of each alternative can be obtained. Furthermore, for the risky multiple decision problem with attribute aspirations, decision maker's aspiration-levels are regarded as the reference points. According to the cumulative prospect theory, the prospect value of each attribute value and decision weight are calculated, respectively, and the comprehensive cumulative prospect value of each alternative can be obtained. On this basis, the overall utility value of each alternative is calculated, and the ranking result of the all alternatives can be determined. Finally, a numerical example is used to illustrate the feasibility and validity of the proposed method.

Key words: management science and engineering, risky multiple attribute decision making, expected utility theory, cumulative prospect theory, attribute aspirations, alternative ranking

摘要： 针对决策者给出部分属性期望的风险型多属性决策问题,提出了一种决策分析方法。在该方法中,首先,依据决策者在各自然状态下给出的属性期望信息,将原始决策问题转化为没有属性期望和具有属性期望的两个独立的风险型多属性决策问题;然后,针对没有属性期望的风险型多属性决策问题,依据期望效用理论,计算各属性下属性值所对应的效用值,进而得到每个方案的综合效用值;进一步地,针对具有属性期望的风险型多属性决策问题,依据累积前景理论,将决策者给出的属性期望视为属性的参照点,进而计算各属性值的前景价值及决策权重函数值并计算每个方案的综合累积前景值;在此基础上,计算得到每个方案的总体效用值,并依据总体效用值的大小对所有方案进行排序。最后,通过一个算例说明了该方法的可行性和有效性。

关键词: 管理科学与工程, 风险型多属性决策, 期望效用理论, 累积前景理论, 属性期望, 方案排序