层次分析法中相对权重的改进算法

Improved Algorithm of Relative Weight in AHP

以层次分析法为背景,分析了确定相对权重的常用算法存在的诸多问题。将和行归一法、方根法与乘幂法相结合,解决了迭代初值的选取问题。将Aitken加速技术引入乘幂法,构建了新的迭代数列,列出了新的算法步骤,解决了线性收敛问题。通过实例对比验证了改进算法的优越性。

On the background of AHP, this paper analyses the common methods in determining relative weight which contain some problems;and then a method combined with both the row vectors sum uniformization, the square-root and the power is put forward for solving the problem of choosing the first iterative value;and thirdly this paper introduces the Aitken accelerated method into the power method, builds a new iterative array and establishes new steps for accelerating convergence. Finally, two examples are given to illustrate advantages of the improved algorithm.