資料型態為指數分配之多屬性決策方法模擬分析比較

多屬性決策方法為管理決策領域中常被廣泛應用之評估技術。然而，多屬性決策方法種類繁多，每個方法所依據的理論也不盡相同，在使用不同的方法應用在同一個問題時，往往可能會產生不同的結果，此為多屬性決策方法常遭非議之處。爰此，研究中透過模擬實驗設計分別以方案數、屬性數、權重分配為模擬參數，並以資料型態是指數分配不研究對象，針對屬性資訊特徵屬於基數型態之間單加權法、層級加權法、ELECTRE法、TOPSIS法及灰關聯分析法五種方法，以排序結果之誤差均方、絕對誤差、最佳方案之一致、排序結果相同之方案數、權重與排序結果之交叉分析及Spearmean等級相關係數七項為衡量準則，進行五種方法之模擬比較。就整體評估而言，在以簡單加權法為基準之下，以ELECTRE法最接近簡單加權法、灰關聯分析法次之，而TOPSIS法相距最遠。此外，透過群集分析法，可將五種方法明顯區分為兩群：簡單加權法、ELECTRE法與灰關聯分析法為一群，層級加權法與TOPSIS法為一群，各群中的方法鄉聲項衡量準則的表現上具有相似的結果。

關鍵字

多屬性決策方法；決策理論；群集分析；模擬

並列摘要

Multiple Attribute Decision Making (MADM) is an evaluation method often used by decision makers and widely used in many management areas. Several methods have been proposed for solving MADM. However, a major criticism of MADM is that different techniques may yield different results when applied to the same problem. In this paper, we run a simulation study suing the number of alternatives and criteria, and choices of weights as the input parameters. The data sets were generated using exponential distributions. We investigate the performances of five methods: Simple Additive Weighting (SAW), Hierarchical Additive (HAW), ELECTRE, TOPSIS and Grey Relational Analysis (GREY) using seven measures of performance, including Menu Squared Error, Mean Absolute Error, top rank matched count, number of rank matched, weighted rank crossing 1, weighted rank crossing 2, and Spearman's correlation for ranks. The results show that, the solutions provided by SAW was used as the benchmark, ELECTRE behaves closer to SAW, followed by GREY, with TOPSIS the least similar to SAW. Furthemore, the cluster analysis shows that, we can cluster the five methods into two groups, with methods in each group yielding similar results.