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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  2. Dempster,A.P(1967).Upper and lower probabilities induced by multi-valued mapping.Annals of Mathematical Statistics,38,325-339.
  3. Shafer,G.(1976).A Mathematical Theory of Evidence.Princeton, New Jersey:Princeton University Press.
  4. Sugeno,M.(1974).Tokyo,Japan,Tokyo Institute of Thchnology.
  5. Wang, Z.,Klir, G. J.(1992).Fuzzy measure theory.New York:Plenum Press.
  6. Zadeh,L.A.(1978).Fuzzy sets as a basic for a theory of possibility.Fuzzy Sets and Systems,1,3-28.
被引用次数
  1. 胡宜中、邱苑慈、林雅惠、王仁宏(2012)。應用模糊積分於國內旅遊網站服務品質之評估。明新學報,38(2),85-105。
  2. 劉湘川(2007)。基於v測度之Choquet積分迴歸模式。測驗統計年刊,15(下),1-14。
  3. 劉湘川(2008)。二階L測度及其Choquet積分迴歸模式。測驗統計年刊,16(上),1-12。
  4. 劉湘川(2008)。基於η完全測度與ε完全測度之Choquet積分迴歸模式。測驗統計年刊,16(下),1-15。
  5. (2006)。λ測度之改進模糊測度及其模糊積分。測驗統計年刊,14(上),15-28。