模糊隨機變數在迴歸模式上的建構

Constructing Regression Model Based on Fuzzy Random Variables

曾能芳(Neng-Fang Tseng)

《智慧科技與應用統計學報》 2卷2期 (2004/12) Pp. 19-38

https://doi.org/10.29807/JTITAS.200412.0002

摘要

傳統迴歸分析是假設觀測值的不確定性來自於隨機現象，本文將模糊隨機變數概念引入傳統迴歸模式，考慮將隨機現象和模糊認知並列研究。針對樣本模糊數(x(下標 i), Y(下標 i))，假設因變數Y(下標 i)為模糊隨機變數，我們稱此為模糊迴歸模式，此結構能充分反映隨機樣本Y(下標 i)的模糊特性。
在模糊隨機變數的架構中，真實隨機變數U之期望值E(U)常是未知的。我們可依據多值邏輯的原則，掘取E(U)的模糊理解，使之成為模糊期望值FE(X)；模糊分配函數FF(下標 X)建構的原理亦同。在本文中將針對模糊迴歸模式，建構模糊因變數Y(下標 i)的模糊期望值和模糊分配函數，用以表達這些未知母數的模糊理解概況。

關鍵字

集合表徵 ； 模糊隨機變數 ； 模糊迴歸模式 ； 模糊期望值 ； 模糊分配函數

並列摘要

Conventional study on the regression analysis is based on the conception that the uncertainty of observed data comes from the random property. Here we consider both of the random property and the fuzzy perception to construct the regression model by using fuzzy random variables. We define response as a fuzzy random variable, and call this model as the fuzzy regression model.
For the concept of fuzzy random variable, the expectation E(U) of the exact random vailable U is allways unknown. By multi-valued logic, we define the fuzzy expectation FE(X) in order to derive the fuzzy perception of E(U). The fuzzy distribution funtion FF(subscript X) is also analogously constructed. Finally we also give the expression for certain important fuzzy statistics such as fuzzy expected value FE(subscript X) and fuzzy distribution function FF(subscript X).

並列關鍵字

Set representation ； Fuzzy random variables ； Fuzzy regression model ； Fuzzy expected value ； Fuzzy distribution function ； Fuzzy unbiased