理想解類似度偏好順序評估方法之延伸及其應用

Extended Topsis Method and Application

10.29973/JCSA.200509.0004

林志娟(Jyh-Jiuan Lin)；劉家佑(Chia-Yu Liu)；張慶暉(Ching-Hui Chang)；林秋華(Chiou-Hua Lin)

多準則決策 ； 理想狀態－反面理想狀態 ； 客觀權重 ； 學生素質 ； MCDM ； ideal and anti-ideal solution ； objective weight

中國統計學報

43卷3期（2005 / 09 / 01）

313 - 336

繁體中文

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.

1. Barron, F.H.,Barrett, B.E.(1996).Decision quality using ranked attribute weights.Management Science,42,515-1523.
2. Charnes, A.,Cooper, W.W.,Rhodes, E.(1978).Measuring the efficiency of decision making units.European Journal of Operational Research,429-444.
3. Chen, S.J.,Hwang, C.L.(1992).Fuzzy multiple attribute decision making: methods and applications.Berlin:Springer-Verlag.
4. Coombs, C.H.(1958).On the use of inconsistency of preferences in psychological measurement.Journal of Experimental Psychology,55,106-118.
5. Deng, H.,Yeh, C.H.,Willis, R.J.(2000).Inter-company comparison using modified TOPSIS with objective weights.Computers & Operations Research,27,963-973.
6. Diakoulaki, D.,Mavrotas, G.,Papayanakis, L.(1995).Determining objective weights in multiple criteria problems: the CRITIC method.Computers & Operations Research,22,763-770.
7. Gagne, R.M.,Briggs, L.J.,Wager, W.W.(1992).Principles of Instructional Design.New York:Harcourt Brace.
8. Hobbs, B.F.(1978).A comparison of weighting methods in power plant citing.Decision Sciences,11,725-737.
9. Hwang, C.L.,Yoon, K.S.(1981).Multiple attribute decision making: method and application. A State-of-the-Art Survey.Berlin, New York:Springer-Verlag.
10. Saaty, T.L.(1995).Decision making for leaders.New York:RWS.
11. Schoemaker, P.J.H.,Waid, C.D.(1982).An experimental comparison of different approaches to determining weights in additive utility models.Management Science,28,182-196.
12. Shannon, C.E.,Weaver, W.(1947).The mathematical theory of communication.Urbana:The University of Illinios Press.
13. Working paper
14. Yoon, K.,Hwang, C.L.(1995).Multiple Attribute Decision Making: An Introduction.California, USA:Sage University.
15. Zeleny, M.(1982).Multiple criteria decision making.New York:McGraw-Hill.
16. 丁在尚(1994)。高師學生素質綜合評價模型及應用。安徽師大學報（自然科學版），17-4，88-90。
17. 孔德芳(1994)。Fuzzy數學在學生素質綜合測評中的應用。濟寧師院學報，3，17-21。
18. 李宏隆(2000)。長榮管理學院經營管理研究所。
19. 林穎、姚夏倩(2000)。以加涅的學生素質觀來素質教育。心理科學，23-2，192-196。
20. 馬曉燕(2003)。模糊綜合評判在學生素質培養制約系統評價中的應用。大學數學，19-1，40-45。
21. 莊豐光(2003)。碩士論文(碩士論文)。國防管理學院國防財務資源研究所。

1. 林建宏、沈維雄(2011)。台灣地區銀行經營績效評估之研究TOPSIS方法之應用。會計與財金研究，4(2)，51-61。
2. 張宗翰、史弼中(2013)。以Entropy-Based TOPSIS評估台灣食品公司經營績效。國立虎尾科技大學學報，31(2)，7-25。