廣義m測度之模糊積分及其在測驗整合計分之應用

Generalized Fuzzy Integrals with Generalized m-measure and their Applications to Obtain the Aggregation Score of the Entrance Examination

劉湘川(Hsiang-Chuan Liu)

《αβγ量化研究學刊》 1卷 (2007/12) Pp. 107-123

摘要

當欲進行綜合評價之多種屬性間具潛在交互作用時，傳統可加性測度分析方法雖計算方便，常功效不彰，此時可考慮採用模糊測度與模糊積分，常用之模糊測度，有Sugeno(1974)之λ測度，及Zadeh（1978）之P測度，其中，λ測度不恆存在非可加性測度，P測度雖恆存在次可加性測度，但靈敏度不足,劉湘川(2006)提出基於P測度之改進模糊測度，稱為m測度，則能兼顧前二者之優點，本文進而推廣改善m 測度之可行解演算法，提出廣義m測度，藉以求取Choquet積分值及Segeno積分值，則可得甚多選擇之整合計分多重決策之可行解法，並以研究所入學測驗整合計分之應用簡例說明之。

關鍵字

λ測度 ； P測度 ； m測度 ； Choquet積分 ； Sugeno積分

並列摘要

When interactions among attributes exist in multiple decision-making problems, the performance of the traditional additive scale method is poor. Non-additive fuzzy measures and fuzzy integral can be applied to improve this situation. The λ-measure (Sugeno, 1974) and P-measure (Zadeh, 1978) are two well-known fuzzy measures. Hsiang-Chuan Liu (2006) pointed out that the λ-measure is not a non-additive fuzzy measure, and the P-measure is a non-additive fuzzy measure with poor sensitivity. Hsiang-Chuan Liu (2006) also proposed an improved non-additive fuzzy measure based on P-measure; called m-measure, which is a non-additive fuzzy measure and more sensible than P-measure.
In this paper, a further improved non-additive fuzzy measure, generalized m-measure, is proposed and this fuzzy measure can generate infinitive non-additive fuzzy measures. Choquet integral and Sugeno integral with this proposed generalized m-measure are applied to obtain the aggregation score of the entrance examination of graduate school.

並列關鍵字

λ-measure ； P-measure ； m-measure ； Choquet integral ； Sugeno integral