模糊DEA排序模式之構建－以銀行分行為評估對象

Abstract

DEA(Data Envelopment Analysis)模式利用明確的產出與投入資料，對各受評估單位（Decision Making Units，簡稱DMUs）進行效率評估，並廣泛應用於許多不同領域之相對效率評估；在實務應用中，投入與產出往往無法以明確值表示，因此過去許多研究結合模糊理論發展出模糊DEA模式，以解決投入項與產出項無法以明確值表示的情況。過去文獻所提出的模糊DEA模式得到的效率值皆以效率區間表示，由於效率值受限於傳統DEA模式之不得超過1的限制，使得模糊效率區間受到限制，無法精確表達DMUs的模糊效率區間，甚至無法針對有效率DMUs加以排序。因此本論文發展出模糊DEA排序模式，精確評估有效率DMUs之模糊效率區間，容許有效率DMUs的效率值大於1。當決策者欲對所有DMUs予以排序時，則本文所提出之模式可以精確地對所有DMUs進行排序，且可兼具提供無效率DMUs改善方向之優點。本文最後以銀行分行效率評估爲例，以證明本文所提出之模糊DEA排序模式之可行性。

The DEA model has been widely applied in performance evaluation using well-defined not always be crisp values and the research has been based on fuzzy theories to develop numerous fuzzy DEA models to deal with non-crisp input-output data. The value obtained using the fuzzy DEA model as reported in literatures is expressed in efficiency that is limited to not exceeding one. This also limits the fuzzy efficiency intervals of DMUs, and the result is hence not capable of expressing the fuzzy efficiency intervals of DMUs precisely. A new Fuzzy DEA Ranking Model is developed in this paper for exactly ranking the efficient DMUs with fuzzy input-output data. This model allows the efficiency values greater than one thus the result precisely shows the fuzzy efficiency intervals for all DMUs, and to rank the efficient DMUs accurately and effectively. Finally, we evaluate the performance of bank branches to exam the practicability and effectiveness of the Fuzzy DEA Ranking Model. The results indicate that this model not only accurately identifies DMU's efficiency intervals but also ranks the efficiency DMUs perfectly.