Abstract: To solve the linguistic-stochastic multi-criterion decision-making problems with incomplete information, a solving method based on one-dimension normal clouds and relative satisfaction degrees was designed. In the method, uncertain linguistic evaluation labels of the alternatives under criteria were transformed into approximate one-dimension normal clouds according to the normal distribution law and the golden section ratio method. By the numerical characteristics variation method, the clouds distances between alternatives and ideal alternative(positive or negative)were measured under the criteria. Through the operation law of interval numbers, the weighted distances between alternatives and ideal alternative(positive or negative)were calculated. The relative satisfaction degrees of the alternatives were gotten, and the ranking order of the alternatives was defined. The urban public transportation network optimization was taken as an example to show the validity and the feasibility of proposed method.

Key words: linguistic-stochastic multi-criterion decision-making, incomplete information, cloud model, ideal alternative, relative satisfaction degree, urban public transportation network optimization

摘要： 为解决不完全信息的语言随机多准则决策问题，设计了一种将一维正态云与相对满意度相结合的求解方法。该方法首先根据正态分布规律与黄金分割率法，将各方案在各准则下的不确定语言评价标度转化为近似的一维正态云；接着采用数字特征差异法，度量在各准则下各方案与正、负理想方案之间云的距离；然后利用区间数的运算法则，求取各方案与正、负理想方案之间的加权距离；最后计算各方案的相对满意度，进而确定排序。以城市公交线网优化为例，验证了该方法的有效性和可行性。

关键词: 语言随机多准则决策, 不完全信息, 云模型, 理想方案, 相对满意度, 城市公交线网优化