以直覺模糊集合為基礎發展多屬性決策之排列評估法

The Permutation Method in Multiple Attribute Decision Making Based on Intuitionistic Fuzzy Sets

陳亭羽(Ting-Yu Chen) ； 湯宇達(Yu-Ta Tang)

《管理科學研究》 7卷1期 (2010/12) Pp. 1-16

https://doi.org/10.6873/MSR.201012_7(1).0001

摘要

多屬性決策分析為個體和群體決策中極為重要的一部分，其問題伴隨著主觀且模糊的存在，因此在實務面受到廣泛討論及應用。本研究乃以直覺模糊集合為基礎來探討多屬性決策問題中的直覺模糊排列評估法，目的在於提出一套新的排列評估法。但是，因所需取得的資料性質屬直覺模糊，資料蒐集困難，得不到完整的決策矩陣，因此嘗試以模擬實驗的方式探討資料蒐集不全時的情境分析。在實驗分析的部份，用簡化決策矩陣及權重的方式，克服資料蒐集的難處，並使用一致率、矛盾率、反轉率與等級相關係數四大指標，比較最後的結果是否和簡化前一致。實驗結果發現，簡化前後的兩個矩陣，前三個指標的平均維持相當高的程度，特別在等級相關係數的部分，呈現出平均值越高，標準差越低的趨勢，代表簡化後的矩陣不會喪失過多的資訊量，兩者的運算結果會越趨一致。

關鍵字

多屬性決策 ； 直覺模糊集合 ； 排列評估法 ； 模擬實驗

並列摘要

The multiple attribute decision making analysis has been widely discussed and applied by means of plenty of empirical works because it plays a crucial role in individual and group decision making problems which contain some subjective and fuzzy nature. The purpose of this study is to propose a new permutation method with intuitionistic fuzzy sets in multiple attribute decision making problems. However, due to the fact that it is not only difficult to obtain intuitionistic fuzzy data, but also incapable of acquiring the complete decision matrix, we use the simulation experiment to discuss the conditions of incomplete data. In the experimental analysis, the simplified decision matrices and weights are employed to overcome the difficulty of data collections. Besides, four indices of the consistency rate, contradiction rate, inversion rate, and Spearman rank order correlation coefficient compare the outcomes between simplified and non-simplified data. The experimental results indicate that the first three indices maintain quite high average values. In particular, the rank order correlation coefficients show the higher the average values, the lower the deviations of average values. It represents the simplified matrices do not lose too much information; instead, the results of computation between simplified and non-simplified data converge eventually.

並列關鍵字

Multiple Attribute Decision Making ； Intuitionistic Fuzzy Set ； Permutation Method ； Simulation Experiment