資訊不完整下層級分析問題之解析─以 0-1 分數規劃法求解

Abstract

傳統的層級分析法 (AHP) 只能解資訊完整下的決策問題。本研究擬以最 佳化方法 (Optima method) 來解決層級分析法在資訊不完整或混淆情形 下的問題。本文先將 AHP 在資訊不完整下的問題轉換成 0-1 分數規劃 (0-1 Fractional Programming) 的問題。此種問題可以線性化成 0-1 規 劃的問題，以分枝─定限 (Branch-bound) 法求得整體最佳解 (Global Optimal Solution) 。另外本文以一些測試的例子，來比較本研究提出的 方法與 Saaty原先提出的層級分析解法。本文之優點為： 1.決策者可不 需設定所有的權值。 2.可求得整體最佳解。 3.允許決策者加入「信心程 度」，以增加模式的可靠性與彈性。 Traditional AHP methods can only slove decision problemswith complete information. This study prposes an optimization thod for solvig AHP problems with icomplete or noisy information. We first transform an AHP problem with incomplete infor- mation into a 0-1 fractional programming problem.This 0-1 fractional programming problem is then linearized as a 0-1 programming which is sloved by a branch-bound method to obtain a global solution. Some numerical testing examples show that the proposal method is superior to Satty's method in following points: 1.decision makers are allowed not to weight all of pairwise criteria. 2.the obtained solution is the global optimal solution. 3.allow a decision maker to specify his "confidence level" and enhance the reliablity and flexibility of AHP method.