探討不完整資訊成對比較矩陣之AHP問題

Abstract

在實際回收層級分析法(AHP)問卷時，常遇到問卷有漏填(miss)的現象，即產生不完整比較矩陣(incomplete pairwise comparison matrix)。而本研究之目的為提出一最佳化工具之基因演算法來估計遺漏值，並且與其相關方法做討論比較，以作為當AHP問卷發生遺漏時，能夠提供解決不完整資訊之AHP問題的參考。對於此問題，過去已有相關的文獻做過探討，是以建立在數學理論的基礎而發展出求解的方法，或是以線性規劃的方式求解，都是為了求出最佳之遺漏值。但未採用基因演算法求解，因此本論文提出另一求解最佳化方法之一的基因演算法來解決此問題。首先，先討論各方法之方法特性，以了解各方法之求解範圍。最後，經由本實驗模擬驗證的結果，可說明與闡釋本論文所提出之各方法在於解決此問題之估計誤差、命中率的績效與程式執行時間，並提供有用的資訊，以作為解決不完整成對比較矩陣之AHP問題的參考，以提升AHP問卷之有效回收率。基於在填回問卷之遺漏值時，估計誤差應越小越好，而基因演算法的估算誤差是小於其他方法，故提出基因演算法在求解不完整成對比較矩陣之AHP問題上的績效是較其他方法兼具有效性與可行性。並期望此研究能作為主要使用AHP問卷之決策者的參考。

In practice, when we retrieve AHP questionnaires, they often run into miss case, i.e. arise incomplete pairwise comparison matrices. The purpose of this study is to address one optimize tool based upon genetic algorithms to approximate missing pairwise comparison value, and we can discuss and compare with related literatures to support the reference of missing problem. With regards to the problem, in the passed, some related researches were based on mathematic theorem or linear programming, which all want to derive the best missing value. But genetic algorithms is another way to deal with the problem, we employ genetic algorithms to automatically find the best missing value. First, in order to understand individual methods of solving domain, we discuss with features of methods. Second, through numerical simulation results, we illuminate that individual performance proposed methods in estimate error , recovered rate and programs running time to provide useful information to refer to solving the AHP problem of pairwise comparison matrix in incomplete information. In conclusion the genetic algorithms is the best way for estimate error and it would be more effective and practicable than others. We expect this research can be mainipulated to assist every decision maker in using AHP questionnaires.