整合層級分析與模糊認知圖之武器系統評選模式

Abstract

決策者所要處理的問題通常具備多重屬性的特性，而存在於屬性之間的關係可能是相互衝突或是互有關聯的，如何解決此等複雜的決策問題，即是一個嚴肅的課題，在許多決策方法之中，層級分析法(AHP)便是一個備受矚目的解決工具。然而AHP為人所詬病的一個缺點即是其對評選屬性獨立性的假設，並且隨著現實問題中屬性關係愈是錯綜複雜，此獨立性假設致使評估結果產生偏差的可能性，恐將愈是加大。本文的目的即在於利用模糊認知圖(Fuzzy Cognitive Maps, FCM)建構AHP中評選屬性的層級結構，致使評選屬性之間的相依性得以事前獲知，並且利用貝氏理論結合AHP 權重及FCM 關聯權重，以妥善處理評選屬性之間的相依性問題，進而使評選過程及結果更能符合實際情況，對於決策者在制定決策時，可以提供最有助益的參考依據。在實務驗證方面，本文以評選武器系統為例，實際驗證所提評選模式的有效性。在建構FCM過程中，特別透過門檻值影響分析，以瞭解門檻值對FCM形成的影響，期能更客觀地建構所需的評選系統。另外，為更進一步瞭解本文所提出評選模式的優勢，特別加入傳統加權平均法與模糊積分法的演算結果與之比較，結果顯示本文所提出的評選模式具有相當的優勢，可提供決策者一個在制定決策時可運用的評選工具。

Decision-making problems are usually multiple-attribute orientated. The relationship between the attributes used may often conflict with one another. Therefore, how to solve these complicate decision-making problems indeed perplexes decision makers. Among the decision-making methods published, Analytic Hierarchy Process (AHP) is a popular tool. However, one of its pitfalls lies in the independence assumption among the attributes. This pitfall would deteriorate the evaluation results as the decision-making problems are complex enough. The purpose of this study aims at employing Fuzzy Cognitive Maps (FCM) to construct a hierarchical structure of independent attributes used in AHP. The distinctive features of FCM employment lie in the prior understanding about the interrelationship between the attributes. As interrelationship existing, Bayes' theorem is utilized to obtain the new weights of attributes by integrating the AHP weights and the FCM weights. As expected, this integration would make the evaluation processes and results fitting in with the real situation. In case verification, the evaluation of weapon system is conducted to show the validation of the integrated model proposed in this study. In constructing FCM, the influence analysis of threshold value is especially conducted to exploit its effect on FCM formation. On the other hand, for further revealing the superiority of this model, the evaluation results come from both the fuzzy integral algorithm and the weighted average operator are compared with those of this model. This comparison verifies the superiority of this model.