- 學位論文
以案例為基礎的TOPSIS有序分類研究
A Study of Case-Based TOPSIS Ordered Classification
摘要
過去TOPSIS在有序分類的應用普遍存在著幾個共同問題：採用的權重常受到決策者的主觀決定，並且進行TOPSIS接近係數排序後，分類切點的制定常是採用過去資料集本身的分類切點來予以分類，這使得整體方法解釋性較差且不夠客觀。我們想要建立一套以案例為基礎的TOPSIS有序分類流程，將備選方案經排序後分類，詳細內容包括制定貼近備選方案本身特性的權重，以增加具有影響力的準則之權重，並提出一個客觀的分類切點設定方法。我們採用的客觀權重制定方法包含：熵權重（Entropy weight）、標準差權重（Standard deviation weight）、標準間相關性權重（CRITIC weight）。我們融合客觀權重及代表性備選方案(即案例)，對資料集進行TOPSIS排序，進而透過線性回歸的概念，以最小化案例的加權分數與可能分類切點的誤差平方和來確定分類切點，並分別使用歐基里德距離、曼哈頓距離作為各備選方案與正負理想解的距離，比較各權重的分類錯誤率。本方法建立在兩個先決條件上：(1) 事先知道此資料集要分為幾類；(2) 有各類別的代表性備選方案。我們以美國傳統基金會的經濟自由指數和UCI 機器學習資料集上的公司破產資料集進行驗證，並得到了滿意的結果。 對於擴充TOPSIS至有序分類，我們整合了權重選擇策略以及由代表性備選方案確定分類切點制定方法，提出新的流程架構，對於TOPSIS應用有更廣泛的延伸。
並列摘要
Previous application of TOPSIS in ordered classification had the following problems: (1) the weights were often affected by the subjective decision of decision makers, and (2) after the computing and sorting of proximity coefficients, the classification cut-off values were borrowed from thresholds of the past data sets. These problems made the overall approach less interpretable and less objective. We would like to establish a case-based TOPSIS ordered classification framework: Firstly, adopt an objective weighting method, reflecting the characteristics of the cases, so that influential criteria are highly weighted. Considered objective weighting methods include: entropy, standard deviation, CRITIC, and equal weights. We integrate objective weights and representative cases to apply TOPSIS sorting for the data set first. We then utilize the concept of linear regression, through minimizing the sum of error squares between the weighted scores of representative cases and possible classification cut-off values, to obtain the optimal classification cut-off values. Both the Euclidean and Manhattan distances from the positive and negative ideal solutions are considered in each weighting scheme. We finally compare the classification error rate of the process. Our framework is based on two prior knowledges: (1) how many categories the cases would be divided into; (2) selected representative cases for each category. We verify the framework with the Heritage Foundation's Index of Economic Freedom and the Corporate Bankruptcy dataset on the UCI Machine Learning dataset, and obtain satisfactory results. This framework provides a wide extension for TOPSIS applications.
參考文獻
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