基于前景理论和隶属度的混合型多属性决策方法

A Method for Hybrid Multiple Attribute Decision Making Based on Prospect Theory and Membership

针对带有决策者期望的混合型多属性决策问题,提出了一种基于前景理论和隶属度的决策分析方法。首先依据决策者对各个属性的期望,将具有清晰数、区间数和语义短语三种形式的决策矩阵转化成为前景决策矩阵。然后,根据各个方案与决策期望之间的广义加权欧氏距离,建立了可变模糊模式识别模型,并通过构造拉格朗日松弛函数,进行交叉迭代计算,得到各个方案的最优隶属度以及对应的属性权重,在此基础上,通过合成各个方案的累计前景值与隶属度,得到方案的综合前景值,并依据综合前景值的大小进行方案排序。最后通过一个原油管道路线优选实例,表明了该方法的可行性与有效性。

An outranking approach for hybrid multiple attribute decision making based on cumulative prospect value and membership is presented. Firstly, the psychological behavioral factors of decision makers are considered, and the expectation of each criterion is chosen as the reference point. Then, the hybrid decision matrix with clear numbers, interval numbers and linguistic assessment terms is transformed into the decision matrix of gains or losses relative to the decision maker＇s expectation. Furthermore, a fuzzy pattern recognition model is built based on weighted euclidean distance between each alternative solution and decision maker＇s expectation. In order to obtain the optimal membership and weight vector, a Lagrange relaxation function is proposed by using cross iterative computations. By synthesizing the comprehensive prospect value and membership, a ranking of each alternative solution is determined. Finally, an oil pipeline route selection example is used to demonstrate how to apply the proposed procedure and comparative studies show its overall ranking consistency.