基于语言判断矩阵的群决策方法

A Group Decision-Making Method Based on Linguistic Judgment Matrices

针对基于语言判断矩阵的群决策问题,提出了一种基于语言信息处理的群决策方法·在描述了基于语言判断矩阵的群决策问题后,通过变量转换关系对语言短语集中的有序语言短语进行"量化",构造了与决策者给出语言判断矩阵"等价的"互反矩阵,利用几何加权平均算法对所得到的互反矩阵进行群集结,并根据和积法求出归一化主特征向量,给出了一种简便的方案排序方法,从而确定最优方案·该方法具有保证传递信息的相对完整性及计算量相对较小的特点·最后通过一个算例说明了该方法的有效性和实用性·

With regard to the group decision-making problems based on linguistic judgment matrices, a new method is proposed. First a reciprocal judgment matrix is constructed equivalent to the linguistic judgment matrix given by decision maker through the transform relation of varizables to quantize the orderly linguistic phrases after describing the group decision-making problem with linguistic judgment matrices. Second, the reciprocal judgment matrices are aggregated regarding the experts' original linguistic judgment matrices by the weighted geometric average judgment matrix method, and then the normalized eigenvetor is obtained by the sum-product method, Meanwhile, a simple algorithm for ranking alternatives is given, and the optimal alternative is determined by ranking the alternatives. The main feature of this method is that it preserves the relative integrality and relative small quantity of calculation in transfering information between linguistic judgment matrices and numerical judgment matrices. Finally, a numerical example is used to illustrate the validity and the applications of the proposed method.