群体选择结果的稳定性分析及其度量方法

群体选择的结果往往受个体主观因素的影响而具有一定的波动性,需要借助某些分析工具来考察其稳定或可靠程度。文中采用几何学方法,针对一类典型、常见的群体选择方法--加权计分规则(weighted scoring rules,WSRs),提出了一种基于评分向量夹角正弦的稳定性分析和度量方法,结合三候选方案情况阐述了该方法的合理性和相关概念的直观几何解释,给出了具体求解方法及其证明,并进一步针对候选方案数不同时可能引起的稳定度可比性问题扩展了相关问题、概念和方法。本文提出的群体选择结果的稳定性度量方法具有较好的直观性和可公度性,可作为多目标群决策问题中稳定性或敏感性分析的一个有力工具。

Analysis and measurement methods of the stability of group decision making

The result of group selection is always unstable with the influence of some individual subjective factors. Thus, it is necessary to analyze the stability or reliability of the decision result by some tools. A geometric measurement method of the stability of weighted scoring rules (WSRs) which are representative group selection rules is proposed based on the inclined angle of two score vectors. Rationality and geometric interpretation of this method are elaborated in the situation that the number of candidates is three, then the computing method of the stability degree and its proof are proposed. Considering the comparability problem of stability degrees with different numbers of candidates, extended concepts and solutions of the stability degree are also discussed. The proposed stability measurement method is well visualized and commensurable. It can be an effective tool of sensitivity or stability analysis in multi objective group decision making problems.