基于泰勒展开的二阶层次分析法初探

经典AHP常用于武器装备效能或能力评估,然而经典AHP采用线性加权模型,即通过底层指标效能线性加权得到顶层指标效能,对非线性体系往往会引入较大评估误差,易产生决策性错误。为解决这一问题,本文以底层指标效能值等于1/2为展开点,给出基于泰勒展开的二阶加权模型,对线性体系,二阶加权模型可退化为经典线性加权模型;推导出二阶AHP的数学表达式,给出二阶AHP效能评估步骤,构建二阶AHP的基本框架。算例表明,二阶AHP评估结果相比经典AHP更接近于解析解,产生决策性错误的机率远小于经典AHP。

Preliminary study of the second order Analytic Hierarchy Process based on Taylor expansion

The classical AHP (Analytic Hierarchy Process) is often used to evaluate the effectiveness or capability of weapons and equipment.However,the classical AHP adopts a linear weighted model,that is,the bottom-level index efficiency can be weighted linearly to get the top-level index efficiency,which often introduces large evaluation errors to the nonlinear system and tends to produce decision-making errors.In order to solve this problem,a second-order weighted model based on Taylor expansion is presented,which takes the efficiency value of the underlying index at 1/2 as the expansion point.For the linear system,the second-order weighted model can be reduced to the classical linear weighted model.The mathematical expression of the second-order AHP is derived,the efficiency evaluation steps of the second-order AHP are given,and the basic framework of the second-order AHP is constructed.The numerical examples show that the evaluation result of the second order AHP are closer to the analytic solution than that of the classical AHP,and the probability of making a decision error is far less than that of the classical AHP.