三参数区间数多属性决策的后悔理论方法
Regret theory approach to multiple attribute decision making with three-parameter interval number

本文将后悔理论方法用于解决三参数区间数多属性决策问题. 首先, 提出一种将三参数区间数转换为两参 数区间数的方法, 避免了传统三参数区间数在大小比较方面不确定信息的遗失. 其次, 依据两参数区间数决策信息 计算不同状态下备选方案及正理想方案各属性的效用值, 从而可得各备选方案的后悔–欣喜值及综合感知效用值. 然后, 针对权重范围已知的情况, 通过构建备选方案综合感知效用最大化优化模型求得属性权重; 针对权重信息完 全未知的情况, 提出一种基于注水原理的属性权重求解方法. 最后, 利用属性权重加权求和方法得到备选方案综合 效用值, 从而通过比较综合效用值得到方案的排序结果.
A kind of regret theory approach is developed for multiple attribute decision making with three-parameter interval number. Firstly, three-parameter interval number is converted into two-parameter interval number before comparison between two three-parameter interval numbers for avoiding loss of uncertain information. Secondly, regret-rejoice value and overall perceived utility value of alternatives are obtained by the utility value of each attribute for alternatives and the positive ideal alternative according to the decision information with two-parameter interval number under different states. Thirdly, if the scope of attribute weights is known，the attribute weights are achieved by constructing a programming model which satisfies the maximum overall perceived utility values of alternatives；if weight information is completely unknown,the attribute weights are got by water-filling theory. Finally overall utility values of alternatives are calculated with weighted sum method, therefore, a ranking of alternatives can be determined by comparison of overall utility value of alternatives.