λ測度之改進模糊測度及其模糊積分

本文指出常用之Sugeno之λ測度有四種缺失:1.不恆存在非可加性測度。2.不同基本事件間之關聯係數λ值均相同，不甚合理。3.不能處理混合非可加性測度問題。4.基本事件間之關聯係數λ值並不能反應基本事件間之實際關聯。本文放寬限制，考慮不同基本事件間可有相異之關聯係數，並以事件間之不同相關係數訂定關聯係數，提出改進上述四種缺失之模糊測度，簡稱為ρ(上標 *)測度，藉以求取Choquet積分值或Segeno積分值，可改進與整合計分有關之決策方法之分析功效。

關鍵字

λ測度； m測度； ρ(上標 *)測度； Choquet積分； Sugeno積分

並列摘要

Sugeno's λ-measure is the most often used fuzzy measure to aggregate criteria in decision making problems with the assumption that there are interactions among criteria. This paper pointed out that Sugeno's λ-measure has following four faults: 1. Its solution of nonadditive measure does not always exist. 2. It is not reasonable that the associative coefficients, λ value, of the different basic events are all equal. 3. It can not be consider to treat the problem of mixture fuzzy measure. 4. The associative coefficients, λ value, of the different basic events can not adequately response the real relation between the different basic events. In this study, we proposed an improved fuzzy measure based on λ-measure by using correlation coefficients replacing associative coefficients, and this improved fuzzy measure, ρ(superscript *)-measure, has overcome above four faults. Furthermore, our proposed ρ(superscript *)-measure is used to calculate two different kinds of fuzzy integral, Choquet integral and Sugeno integral, for student's performance based on a Basic Competence Test in four simple examples. The results show that ρ(superscript *)-measure is more useful then λ-measure and m-measure to aggregate criteria in decision making problems when the interactions among criteria exist.