基於P測度之改進模糊測度及其模糊積分

An Improved Fuzzy Measure Based on P Measure and Its Fuzzy Integrals

10.6773/JRMS.200606.0001

劉湘川(Hsiang-Chuan Liu)

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

測驗統計年刊

14期_上（2006 / 06 / 01）

1 - 14

繁體中文

在模糊測度中，常用之Sugeno之λ測度雖靈敏，但不恆存在非可加性測度，Zadeh之P測度，恆存在非可加性測度，且計算簡易，但測度較不靈敏，且只能處理特定之次可加性測度。本文提出基於P測度之改進模糊測度，則能兼顧前二者之優點，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。

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. It is a sensitive fuzzy measure. But its solution of nonadditive measure does not always exist. Zadeh's P-measure always has the easy computing solution of nonadditive measure. But its solution of non-additive measure is not sensitive enough as the Sugeno's λ-measure. In this study, we propose an improved fuzzy measure based on P-measure and its solution of nonadditive measure is not only always existed but also easy computed and sensitive. Three fuzzy measures, including λ-measure, P-measure, and our proposed m-measure are used to calculate two different kinds of fuzzy integral, Choquet integral and Sugeno integral for student’s performance based on a Basic Competence Test by 10 simple examples. The results show that our proposed m-measure is the best among the three fuzzy measures to aggregate criteria in decision making problems when the interactions among criteria exist.

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