一种新型不确定AHP的研究与应用

Research on and application of new uncertainty model in analytical hierarchy process

针对现有AHP方法在某些决策环境下不能准确反映决策者的偏好,以及群决策背景下专家偏好集结的信息丢失等问题,研究元素服从离散分布的一种新型不确定AHP,将未确知数概念引入到AHP之中,用局部一致性和整体一致性思想检验未确知数判断矩阵,并根据未确知数判断矩阵的特点,提出基于未确知数运算法则和蒙特卡罗模拟的两种权重求解方法,最后通过两个例子说明新方法的应用可行性.

Decision-makers＇ preferences cannot be expressed correctly sometimes either via the original approaches or their extensions in the Analytical Hierarchy Process （AHP） under some uncertain decision environments. In addition, information distortion is inevitable when integrating multiple experts＇ preferences. To solve these problems, comparison matrices following discrete distribution are studied, and unascertained numbers are introduced into the matrix. Moreover, the consistency property of the unaseertained number comparison matrix is analyzed. The local consistency indexes and the whole consistency indexes are developed to test the consistency of the unascertained numbers matrix. Two weighting approaches are put forward based on the property of this new uncertain model. One is based on the calculation rule of unascertained numbers, and the other is via the Monte Carlo simulation approach. The practicality is illustrated two examples.