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題名：模糊資料包絡分析模式之求解與應用
作者：劉祥泰
作者(外文)：Shiang-Tai Liu
校院名稱：國立成功大學
系所名稱：工業管理學系
指導教授：高強
學位類別：博士
出版日期：1999
主題關鍵詞：資料包絡法；效率；模糊集合；排序；data envelopment analysis；efficiency；fuzzy set；ranking
原始連結：連回原系統網址new window
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自資料包絡分析模式提出後，各領域均廣範應用此模式來評估相對效率，也確實得到很好的結果。當資料包絡分析模式中的投入或產出項為口語化述詞或模糊數值時，則模式即成為模糊資料包絡分析模式。
研究中利用截集及擴展法則，將模糊資料包絡分析模式簡化成一對含有水準參數的傳統資料包絡分析模式。在特定的水準下，可利用這一對模式求解效率值的上下限；藉由多個不同水準的效率值解，即可構建出效率值的隸屬函數。由於以隸屬函數形式表達效率值解，包含最樂觀、最悲觀及最有可能之效率值區間，因此能提供管理者更豐富之資訊。研究中也同時探討模糊資料包絡法相關之效率改進、技術效率與規模效率等求解方向。
由於應用模糊資料包絡法所求得的效率值為模糊數值，所以很難直接依效率值的大小將受評單位排序，且因無法獲知效率值隸屬函數之確切形式，故研究中應用 「面積估量法」與「最大及最小集合法」兩種模糊數值排序的方法，來解決模糊效率值排序的問題。
本文最後以國內大學圖書館績效評估及機械業效率評估為應用實例，分別說明在資料不全及口語化述詞資料情形下，如何應用模糊資料包絡法評估相對績效或效率。從實際案例的應用中得知：在模糊環境下，模糊資料包絡法是效率評估的有效方法。
Since its development in 1978 by Charnes, Cooper, and Rhodes data envelopment analysis has been widely applied to different areas for evaluating the efficiency of multiple-input and multiple-output decision making unit (DMU). The existing DEA models are limited to crisp data. This research proposes a procedure to measure the efficiencies of DMUs with fuzzy observations.
The idea is based on the -cuts and extension principle to reduce a fuzzy DEA model to a family of crisp DEA models, which can be described by a pair of parametric programs, to find the lower and upper bounds of the efficiency measures at  level. From different possibility levels , the membership functions can be derived correspondingly. Due to the efficiency measures are expressed by membership functions rather than crisp value, more information is provided for management. The solution procedures for efficiency improvement, technical efficiency, and scale efficiency in fuzzy DEA model are also proposed.
Since the efficiencies calculated are also fuzzy numbers, appropriate ranking methods are required to determine the order of each DMU. Two methods for ranking are discussed in this study. One is the area measurement method which does not need to know the exact form of the membership functions. Another is the maximum set and minimum set method which usually is applied when the membership functions are known. Via a skillful modeling technique, the requirement of the membership functions is avoided.
The evaluation of Taiwan’s twenty-four university libraries with missing data and the efficiency measures of Taiwan’s fifteen machinery firms with linguistic terms are illustrated, respectively, to demonstrate how the fuzzy DEA model is applied to calculate the efficiency scores. It is shown that the fuzzy DEA model is an effective approach to measure the relative efficiencies under fuzzy environment.
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