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題名 | 基於ν測度之Choquet積分迴歸模式=The Choquet Integral Regression Model Based on ν-Measure |
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作者 | 劉湘川; Liu, Hsiang-chuan; |
期刊 | 測驗統計年刊 |
出版日期 | 20071200 |
卷期 | 15(下) 2007.12[民96.12] |
頁次 | 頁1-14 |
分類號 | 319 |
語文 | chi |
關鍵詞 | λ測度; P測度; ν測度; Choquet積分; Choquet積分迴歸模式; λ-measure; P-measure; ν-measure; Choquet integral; Choquet integral regression model; |
中文摘要 | 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)l 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、r 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「n 測度」,進而提出基於 n 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。 |
英文摘要 | Abstract When interactions among criteria exist in multiple decisionmaking problems or forecasting problems, the performance of the traditional additive scale method is poor. Nonadditive fuzzy measures and fuzzy integral can be applied to improve this situation. Thel measure (Sugeno, 1974) and Pmeasure (Zadeh, 1978) are the most often used fuzzy measures, HsiangChuan Liu (2006a) pointed out that thel measure does not always exist the solution of nonadditive fuzzy measures, and the Pmeasure has poor sensitivity. HsiangChuan Liu (2006a, b, c, d) has sequentially proposed three improved nonadditive fuzzy measures; m measure, r * measure, polyvalent m measure. This paper pointed out that there are nonconsistence between the definitions of measures of joint events and the measures of basic events and empty event in previous three improved nonadditive fuzzy measures. In this paper, the improved nonadditive fuzzy measures, n measure, with completely consistent measure definitions for all events is proposed and a new Choquet integral regression model based on this n measure is also proposed. |
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