多元Fuzzy线性回归

在处理某些系统模型中,有些输出或输入量的值是通过人的心理测量给出的。这时我们可认为此系统具有Fuzzy结构。这种Fuzzy结构一般可用带有Fuzzy参数的Fuzzy线性函数表示,而Fuzzy线性函数可由Zadeh的扩展原理得到。这样用Fuzzy线性函数来描述系统的Fuzzy结构便形成了Fuzzy线性回归分析。当输出输入量均是多个时便是多元Fuzzy线性回归。在经典的多元回归中,观测向量值与估计向量值之间的差异一般认为是测量误差,本文处理的多元Fuzzy回归中,我们认为其差异是由于系统的Fuzzy性造成的而反映在回归方程的Fuzzy参数上,这种Fuzzy参数一般表示一种可能性分布。文章讨论了多元Fuzzy回归模型的拟合问题,给出了其Fuzzy向量参数的估计方法,并将其计算方法归结为求解某线性规划问题。本文使用的Fuzzy向量限制在三角族内,而对其它形式的常用Fuzzy向量也没有实质困难。

Multivariate Fuzzy Linear Regression

In modeling some systems where some values of inputs and outputs are grven by person's psychological measurement, we must deal with a fuzzy structure of the system considered. This structure is represented as a fuzzy linear function whose perameters are fuzzy. The fuzzy linear functions are defined by Zadeb's extension principle. Considering a fuzzy linear funtion as a model of fuzzy structure of the system, a fuzzy linear regression analysis is formulated 1-4]. When the output is not single, the multivariate fuzzy linear regression is obtained. In classical multivariate regression, the deviations between the estimated vactor and the measured vactor are regared as the observation errors, but, in this paper, the deviations are regared as the fuzziness of the system which are reflected in the fuzzy parameters, the fuzzy parameter usually means a possibility distribution. In this paper, we discuss the fitting of the multivariate fuzzy regression model and give the method of estimating the fuzzy parameters which can be transformed into a linear programming problem to solve.