属性权重未知的连续风险型多属性决策研究

针对属性权重未知、属性值为有限区间上的连续随机变量的风险型多属性决策问题,提出了一种灰色关联度排序方法。首先,通过密度函数的变换,对风险决策矩阵进行规范化处理,并通过期望值定义了两个随机变量之间的偏差,利用离差最大化原则确定了属性指标权重。然后定义了正负理想解,计算每个方案与正负理想解的灰色关联度及相对贴近度,根据每个方案的相对贴近度确定方案排序。最后,给出了以属性值为区间数的多属性决策问题的决策步骤,证明了该方法的有效性。

Research on multiple attribute decision-making under risk with continuous random variable and weight unknown

A grey correlation rank method is presented to solve the problems of multiple attribute decision-making(MADM) under risk with weight unknown and attribute value as continuous random variable on bounded intervals.To begin with,the risk decision matrix is normalized by density function,a deviation between two random variables is defined by expectation value,and the maximizing deviation rule is used to determine the weights of attributes.Then,positive/negative ideal solutions are defined.The grey correlation degrees between alternatives and positive/negative ideal solutions and the relative closeness coefficients are calculated.Furthermore,the alternatives are ranked by the relative closeness coefficients of alternatives.Finally,an MADM example with interval number is given to demonstrate the steps and effectiveness of the proposed method.