基於ν測度之Choquet積分迴歸模式

The Choquet Integral Regression Model Based on v-Measure

劉湘川(Hsiang-Chuan Liu)

《測驗統計年刊》 15期_下 (2007/12) Pp. 1-14

https://doi.org/10.6773/JRMS.200712.0001

摘要

當欲進行綜合評價之多種屬性間具潛在交互作用時，傳統可加性測度分析方法雖計算方便，常功效不彰，此時應考慮採用模糊測度與模糊積分，常用之模糊測度，有Sugeno (1974)λ之測度、Zadeh (1978)之P測度，劉湘川(2006a)指出測度不恆存在非可加性測度，P測度靈敏度不足，劉湘川(2006a, b, c, d)先後提出具靈敏度且恆存在非可加性測度之逐次改進模糊測度；二值m測度、ρ測度、多值m測度，本文指出多值m測度之聯合事件模糊測度之定義未兼顧基本事件測度之一致性，特提出改進之模糊測度，稱為「v測度」，進而提出基於v測度之Choquet積分迴歸模式，將有利於具潛在交互作用資料之綜合評價與預測分析。

關鍵字

λ測度 ； P測度 ； v測度 ； Choquet積分 ； Choquet積分迴歸模式

並列摘要

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 (Sugeno, 1974) and P-measure (Zadeh, 1978) are the most often used fuzzy measures, Hsiang-Chuan Liu (2006a) pointed out that the λ-measure does not always exist the solution of non-additive fuzzy measures, and the P-measure has poor sensitivity. Hsiang-Chuan Liu (2006a, b, c, d) has sequentially proposed three improved non-additive fuzzy measures; m-measure, ρ*-measure, polyvalent m-measure.
This paper pointed out that there are non-consistence between the definitions of measures of joint events and the measures of basic events and empty event in previous three improved non-additive fuzzy measures.
In this paper, the improved non-additive fuzzy measures, v-measure, with completely consistent measure definitions for all events is proposed and a new Choquet integral regression model based on this v-measure is also proposed.

並列關鍵字

λ-measure ； P-measure ； v-measure ； Choquet integral ； Choquet integral regression model

參考文獻

翁惟盛、張凱怡、林文質、劉湘川()。

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。14，1-14。

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。14，1-14。

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。14，15-28。

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。14，15-28。