区间值模糊随机多准则决策方法

针对不完全信息的区间值模糊随机多准则决策问题，提出了两种求解方法。第一种方法利用离差最大化构建区间参数线性规划，通过区间数运算法则和定位规划求得最优准则权重向量、状态集结值区间决策矩阵与期望值区间决策矩阵，根据决策者风险偏好水平得到各方案的期望集结值从而确定排序。第二种方法将区间值模糊数决策矩阵转化为直觉模糊数决策矩阵，利用不完全的准则权重，通过规划模型求解，获取各方案在各自然状态下的加权记分函数值与加权精确函数值的区间，利用不完全的状态概率，得到各方案的记分函数期望值与精确函数期望值的区间，根据决策者风险偏好水平，求得各方案的记分函数与精确函数的期望集结值，进而确定方案的排序结果。算例分析验证了两种方法的有效性和可行性。

Methods of interval-valued fuzzy-stochastic multiple-criterion decision-making problem

To solve the interval-valued fuzzy-stochastic multiple-criterion decision-making problems with incomplete information, two methods are suggested. In the first method, a linear programming model with interval parameters is constructed based on maximal deviations. The optimal weight vector, decision-making matrix consisting of integrated interval values in the states, and decision-making matrix consisting of expected interval values are successively worked out by the operation rules of interval numbers and the located programming model. According to the risk preference level of decision-makers, the expected integrated values of alternatives are gotten. In the second method, the decision matrices with interval-valued fuzzy numbers are transformed into the decision matrices with intuitionistic fuzzy numbers. According to the incomplete criterion weights and programming model, the evaluation intervals of the weighted score functions and the weighted accuracy functions of the alternatives are worked out under the states. The expected evaluation intervals of the score functions and the accuracy functions of the alternatives are gotten through the incomplete state probabilities. With the help of the risk preference levels, the expected integrated evaluations of the score functions and the accuracy functions of the alternatives are attained. In the methods, the rank order of the alternatives comes out in the end. A numeric example shows the validity and the feasibility of the methods.