基于前景M-V准则的正态三角模糊随机多属性决策方法

Approach for normal triangular fuzzy stochastic multiple attribute decision making based on prospect mean-variance rule

针对具有正态三角模糊随机变量且属性权重未知的多属性决策问题,提出基于前景均值-方差(M-V)准则的正态三角模糊随机多属性决策方法.该方法首先构建正态三角模糊随机决策矩阵,进而通过运算得到属性值的期望与方差,并将其转化为M-V决策矩阵;然后,通过定义前景效应构建前景M-V决策矩阵,利用改进灰色系统理论模型求解属性权重值,获取综合前景M-V决策矩阵;最后,定义前景序关系,两两比较前景M-V价值获取方案排序.在此基础上,通过案例验证了所提出方法的可行性及有效性.

With respect to the problem of multiple attribute decision making, in which attribute weights are unknown and attribute values are given in terms of normal triangular fuzzy stochastic variables, an approach for normal triangular fuzzy stochastic multi-attribute decision making is proposed based on the prospect mean-variance rule. Firsdy, a normal triangular fuzzy stochastic decision matrix is constructed. A mean-variance decision matrix is then obtained by calculating the expectation and variance of the normal triangular fuzzy stochastic decision matrix. Secondly, a prospect effect is defined, and a prospect mean-variance matrix is built by setting an attribute reference point of each alternative. Moreover, an improved grey system theory model is built to determine the attribute weights. The prospect mean-value matrix is transformed into a comprehensive prospect mean-variance matrix. Finally, according to the prospect order relation defined, a ranking of alternatives is obtained. A practical example is given to show the feasibility and effectiveness of the proposed approach.