二階L測度及其Choquet積分迴歸模式

Second-order L-Measure and Its Choquet Integral Regression Model

10.6773/JRMS.200812.0001

劉湘川(Hsiang-Chuan Liu)

λ測度 ； v測度 ； L測度 ； 二階L測度 ； Choquet積分迴歸模式 ； λ-measure ； v-measure ； L-measure ； second-order L-measure ； Choquet integral regression model

測驗統計年刊

16期_上（2008 / 12 / 01）

1 - 12

繁體中文

當綜合評價之多種屬性間，具有潛在交互作用時，傳統可加性測度方法表現欠佳，可考慮採用模糊測度與模糊積分。進行模糊積分前，須先選擇適當之模糊測度，眾所周知Sugeno之λ測度與Zadeh之P測度均只有唯一解，劉湘川先後提出逐次改進之三種多值模糊測度；「μ測度」、「v測度」及「L測度」，上述三種多值模糊測度均可有無限多模糊測度之解可供選擇。本文在L測度之定義式中添加「平方指標」以增進靈敏度，提出進一步改進之「二階L測度」，同時亦提出「基於二階L測度之Choquet 積分迴歸模式」，將更有利於具潛在交互作用資料之綜合評價與預測分析。

When interactions among criteria exist in multiple decision-making problems or forecasting 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 proposed by Sugeno and the P-measure proposed by Zadeh, are the most often used fuzzy measures, but the above two measures both have only one solution of fuzzy measure. Hsiang-Chuan Liu has proposed three polyvalent fuzzy measures: μ-measure, v-measure and L-measure. All of the three improved measures have infinite many solutions of fuzzy measures. In this paper, A square index is adding to two terms in formula of the L-measure for being more sensitive then L-measure, and get an improved fuzzy measures, called ”second-order L-measure”, and a new Choquet integral regression model based on this second-order L-measure is also proposed.

1. 劉湘川(2006)。基於P測度之改進模糊測度及其模糊積分。測驗統計年刊，14(1)，1-15。
   連結：
2. 劉湘川(2006)。λ測度之改進模糊測度及其模糊積分。測驗統計年刊，14(1)，16-34。
   連結：
3. 劉湘川(2006)。λ測度之改進模糊測度及其模糊積分。測驗統計年刊，14(1)，16-34。
   連結：
4. 劉湘川(2007)。基於v測度之Choquet積分迴歸模式。測驗統計年刊，15(2)，1-17。
   連結：
5. 劉湘川(2006)。基於P測度之改進模糊測度及其模糊積分。測驗統計年刊，14(1)，1-15。
   連結：
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