一种新的求解区间数判断矩阵权重的方法

研究区间数判断矩阵的一致性和权重求解新方法.基于权重可行域定义了区间数判断矩阵局部一致性和局部满意一致性,并建立了判别其是否具有局部满意一致性的数学模型.作为度量区间数判断矩阵一致性优劣的一种有效方法,给出了区间数判断矩阵一致性程度的概念,并对一致性程度较差的区间数判断矩阵提出一种改进方法.以在区间数判断矩阵内搜索一致性水平最好的确定性判断矩阵为目标建立一个新的权重模型,求解此确定性判断矩阵的权重,以此作为区间数判断矩阵的权重,模型由颗粒群算法求解.最后给出了一个例子说明本文方法的有效性.

Novel Weight Approach for Interval Numbers Comparison Matrix in the Analytic Hierarchy Process

New consistency definitions and weight approach deriving from the interval numbers comparison matrix in the analytic hierarchy process are studied. First, define the local consistency and the local satisfactory consistency based on the idea of weight feasible region. Second, put forward a model to check whether the interval numbers comparison matrix has the local satisfactory consistency or not. Third, define the consistency degree to check the whole consistency and suggest a modification approach to adjust the interval numbers matrix with the bad consistency degree. Finally, a new approach for deriving weight from the interval numbers matrix is proposed. The objective is to seek a crisp matrix from the interval numbers matrix with the minimum consistency ratio. Then, the weight deriving from the crisp matrix can be regarded as the weight for the interval numbers matrix, which is solved by the particle swarm optimization. An example is given to illustrate the approach.