A Comparative Analysis of Objective Weighting Methods with Intuitionistic Fuzzy Entropy Measures

以直覺模糊熵測度發展客觀權重法之比較性分析

10.29977/JCIIE.200911.0005

陳亭羽(Ting-Yu Chen)；李佳航(Chia-Hang Li)

直覺模糊熵 ； 決策 ； 客觀權重 ； 直覺模糊集合 ； 比較性分析 ； intuitionistic fuzzy entropy ； decision making ； objective weight ； intuitionistic fuzzy set ； comparative analysis

工業工程學刊

26卷6期（2009 / 11 / 01）

469 - 479

英文

相較於傳統熵測度著重屬性的區辨程度，本研究利用直覺模糊熵測度具備可信度的特質發展一套新的客觀權重方法以解決多屬性決策問題。我們運用Vlachos與Sergiadis[18]以及Zeng與Li [25]所提出最新的直覺糢糊熵測度作爲本研究方法的基礎架構，而研究中的直覺糢糊熵測度均是以直覺模糊集合隸屬程度與非隸屬程度的觀點以計算得出直覺模糊熵值。經由模擬實驗的比較性分析，我們探討當不同屬性個數與方案個數的組合之下，使用相異的直覺模糊熵測度於客觀權重法所產生的結果。實驗數值顯示本研究所提出的客觀權重法執行不同的直覺模糊熵測度時會計算出相異的屬性權重值與排序，即使這些直覺模糊熵測度源自相同定理也會產生具有差異的權重，值得一提的是實驗所設定的屬性個數能夠影響直覺模糊熵測度之間的相似程度。本研究多屬性的客觀權重法不僅可計算客觀權重，更能結合決策者的主觀權重以獲得一個折衷的屬性權重值。

Instead of the traditional entropy measures which focus on the discrimination of attributes, we utilize the nature of intuitionistic fuzzy (IF) entropy measures which assess the weight of attributes based on the credibility of data to propose a new objective weighting method for solving the multiple attribute decision making (MADM) problems. In this proposed method, we executed various and the newest IF entropy measures introduced by Vlachos and Sergiadis [18], and Zeng and Li [25]. Both of them estimated the IF entropy from the viewpoint of membership and non-membership degree of intuitionistic fuzzy sets. A comparative analysis of experimental simulation which contains not only different combinations of given number of attributes and alternatives but also different IF entropy measures is designed to observe and discuss the outcomes. The experimental results indicated that different IF entropy measures applied in the weighting method would generate distinct weight values and the ranking of attributes even though the measures originated from the same theorem. Especially, the number of attributes decides the extent of similarity among IF entropy measures. With the new objective weighting method, the decision maker can combine it with his/her subjective weights to obtain a compromise attribute weights in MADM problems.

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