多評準決策結合模糊決策圖結構化模型問題之研究

Abstract

決策制定的過程中包含一系列問題的標示、建立優先順序的條件，然後再評估其中最佳的選項。當問題僅限制在單一評準的條件下作決策，它可以很直覺的作判斷，只要找出最佳評準的選項即可。但是，當決策者在評估多評準中評估選項時，必須考慮許多問題面向，例如：評準選項的權重、選項之間的相依性、選項之間彼此之間的衝突性，這些特質會使得針對問題作決策時，變得非常的複雜。因此，必須有對應的方法來處理這些問題。多評準決策(multi-criteria decision making, MCDM)意味著決策者必須在多選項、衝突的、交互影響的選項中作決定。傳統上的研究是應用多屬性效用理論(multiple attributes utility theory, MAUT) 來處理MCDM的問題。MAUT的主要缺陷在於它假設評準選項之間，彼此之間必須獨立無交互影響，此項假設與處理現實問題時有明顯差鉅。目前，有兩個主要的方法可以處理選項之間有交互影響關係，分別為分析網路程序法(analytic network process, ANP)與決策實驗室分析法(decision making trial and evaluation laboratory, DEMATEL)。 分析網路程序法(ANP)，應用在克服目標或選項之間有著相依性或自我回饋機制等特質的問題。ANP是層級分析法(analytic hierarchy process, AHP)的一般通式。AHP是利用階層式架構，推導出選項或評準的權重，但彼此之間必須是相互獨立的。因此，當決策問題涉及彼此之間有相依性與自我回饋時，就必須使用ANP。雖然ANP被廣泛使用在不同領域的應用中，但它存在著兩個主要的缺點，分別為選項或目標的必須相互比較，與必需要事先決定選項或評準間的關係結構。另外一個解決選項或目標相依性問題的方法是DEMATEL，它的主要缺點則是假設每一階段的變化必須是線性的，而且它不可能處理自我回饋機制的問題。 在本論文中，我們提出模糊決策圖(fuzzy decision maps, FDM)的方法。它是結合特徵值(eigenvalue) 、模糊認知圖(fuzzy cognitive maps, FCM)、與權重方程式等方法，來處理並克服相依性與ANP的缺陷。在利用數學的證明與實例佐證中，FDM可以被視為DEMATEL的一般化型態。本論文中，舉一個真實的個案來詮釋FDM的方法，此個案的應用為在評估企業知識資本中的權重。

Decision-making process involves a series of identifying the problems, constructing the preferences, evaluating the alternatives, and determining the best alternative. It is extremely intuitive while considering the single criterion problems, since we only need to choose the alternative with the highest preference rating. However, when decision makers evaluate the alternatives with the multiple criteria, many problems, such as weights of criteria, preference dependence, and conflicts among criteria, seem to complicate the decision problems and should be overcome by more sophisticate methods. Multi-criteria decision making (MCDM) involves determining the optimal alternative among multiple, conflicting, and interactive criteria. Many methods, which are based on multiple attribute utility theory (MAUT), have been proposed (e.g. the weighted sum and the weighted product methods) to deal with the MCDM problems. The main problem of MAUT is the assumption of preferential independence. Two major methods could use to solve preferential independence problem that are analytic network process (ANP) and decision making trial and evaluation laboratory (DEMATEL). The analytic network process (ANP) was proposed to overcome the problem of dependence and feedback among criteria or alternatives. The ANP is the general form of the analytic hierarchy process (AHP). AHP was proposed to derive the relative weights according to the appropriate hierarchical system with preferential independence. Although the ANP have been widely used in various applications, two main problems should be highlighted as follows. The first is the problem of comparison. The second is the key for the ANP is to determine the relationship structure among features in advance. Another approach to deal with the interdependence among the criteria is using the DEMATEL (Decision Making Trial and Evaluation Laboratory) method. The major shortcoming of the DEMATEL method is to assume the criteria-iteration states may be interactive linearly and no feedback loops will allow in relationship maps. In this dissertation, we proposed the fuzzy decision maps (FDM), which incorporates the eigenvalue method, the fuzzy cognitive maps (FCM), and the weighting equation, to overcome the problem of preferential independent and the shortcomings of the ANP. On the basis of the mathematical proof and numerical results, we can conclude that FDM is a generalization of DEMATEL method. A real world case, value assessment for knowledge capital of enterprises, is implemented to demonstrate the FDM method.