如何同時綜合不同準則且有效地評估方案及排序呢？本研究主要是從Hwang和Yoon(1981)在多凖則決策(Multiple Criteria Decision Making, MCDM)的“理想狀態－反面理想狀態”(Ideal and Anti-ideal)概念出發，以及根據Deng，Yeh和Willis(2000)文中所提出的理想解類似度偏好順序評估調整法(Modified Technique for Order Preference by Similarity to Ideal Solution Method)加以延伸，並利用各方案在不同準則下之評分爲資料，以準則相對重要性與理想解偏好順序之距離兩種成份構造出加權距離函數，作爲多準則決策之評估依據。其中距離的定義除了歐幾里德距離外還加了Sinha(2003)建議的城市街道距離之考量，對於客觀加權距離的選擇，本研究探討等權重距離法(Equal Weight Distance Method)、熵值權重距離法(Entropy-Based Distance Method)、變異係數權重距離法(C. V. -Based Distance Method)及平均綜合指標法等四種不同方法的適用性。並將之應用在某大學入學成績各科系平均分數表現的順序評估上：除了計算各系學生入學成績至理想狀態、反面理想狀態的加權距離，並透過其所形成的綜合指標將各系加以排序，以衡量各系學生的素質。據以提供學校一個簡單、客觀的學生素質評估的總指標。
Simultaneous consideration of multiple attributes and reaching an "optimal" solution is not an easy task. How to evaluate students' academic performance is also an important issue. The scope and purpose of this research is to propose a method to determine reliable objective weights for the performance evaluation and ranking of students according to the entrance exam scores which are supposed to evaluate different capabilities in various subjects. The approach used in the research basically adopt the "ideal and anti-ideal solution" concept from Hwang and Yoon (1981) in MCDM (Multiple Criteria Decision Making) and extend the method so called TOPSIS (Technique fur Order Preference by Similarity to Ideal Solution Method). The objective weights choices associated in this research are mean, entropy-based and c.v.-based. In addition to Euclidian weighted distance, city block weighted distance as suggested by Sinha (2003) will he introduced into the indices calculation model. A case study about the entrance exams scores of the University will he conducted using the above-mentioned method.
中國統計學報=Journal of the Chinese Statistical Association 43(3)，頁313-336