Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least squares estimates

Authors:
Ralf Körner;Wolfgang Näther
Affiliations:
Faculty of Mathematics and Computer Sciences, Freiberg University of Mining and Technology, 09596 Freiberg, Germany;Faculty of Mathematics and Computer Sciences, Freiberg University of Mining and Technology, 09596 Freiberg, Germany
Venue:
Information Sciences: an International Journal
Year:
1998

Citing 4
Cited 6

Fuzzy data analysis by possibilistic linear models

Fuzzy Sets and Systems - Fuzzy Numbers
Fuzzy least squares

Information Sciences: an International Journal
On the variance of fuzzy random variables

Fuzzy Sets and Systems
Optimization by Vector Space Methods

Optimization by Vector Space Methods

Weighted fuzzy ridge regression analysis with crisp inputs and triangular fuzzy outputs

International Journal of Advanced Intelligence Paradigms
A hybrid fuzzy regression-fuzzy cognitive map algorithm for forecasting and optimization of housing market fluctuations

Expert Systems with Applications: An International Journal
Fuzzy Statistical Analysis of Multiple Regression with Crisp and Fuzzy Covariates and Applications in Analyzing Economic Data of China

Computational Economics
Kernel based nonlinear fuzzy regression model

Engineering Applications of Artificial Intelligence
A two-stage approach for formulating fuzzy regression models

Knowledge-Based Systems
A unified approach to asymptotic behaviors for the autoregressive model with fuzzy data

Information Sciences: an International Journal

Quantified Score

Hi-index	0.07

Visualization

Abstract

This paper deals with problems which arise if for well justified statistical models like linear regression only fuzzy data are available. Three approaches are discussed: The first one is an application of Zadeh's extension principle to optimal classical estimators. Here, the result is that they, in general, do not keep their optimality properties. The second one is the attempt to develop a certain kind of linear theory for fuzzy random variables w.r.t. extended addition and scalar multiplication. The main problem in this connection is that fuzzy sets, with these extended operations, do not constitute a linear space. Therefore, in the third approach, the least squares approximation principle for fuzzy data is investigated, which leads to most acceptable results.