题名 |
λ測度之改進模糊測度及其模糊積分 |
并列篇名 |
An Improved Fuzzy Measure Based on λ-Measure and Its Fuzzy Integrals |
DOI |
10.6773/JRMS.200606.0015 |
作者 |
劉湘川(Hsiang-Chuan Liu) |
关键词 |
λ測度 ; m測度 ; ρ(上標 *)測度 ; Choquet積分 ; Sugeno積分 ; λ-measure ; m-measure ; ρ(superscript *)-measure ; Choquet integral ; Sugeno integral |
期刊名称 |
測驗統計年刊 |
卷期/出版年月 |
14期_上(2006 / 06 / 01) |
页次 |
15 - 28 |
内容语文 |
繁體中文 |
中文摘要 |
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。 |
英文摘要 |
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. |
主题分类 |
基礎與應用科學 >
統計 社會科學 > 教育學 |
参考文献 |
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被引用次数 |