Fuzzy prediction based on regression models

doi:10.1016/0020-0255(82)90043-3

Information Sciences

Volume 26, Issue 1, February 1982, Pages 45-63

https://doi.org/10.1016/0020-0255(82)90043-3 Get rights and content

Abstract

We use a linguistic variable to represent imprecise information to be inserted in regression models used for prediction. We show how one can obtain probabilistic statements about the forecasted variables.

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Citation Excerpt :
Kim and Bishu (1998) used a criterion of minimizing the difference of the membership degrees between the observed and estimated fuzzy numbers. Yager (1982) used a linguistic variable to represent imprecise information for the regression models. Bárdossy (1990) proposed many different measures of fuzziness which must be minimized with respect to some suggested constraints.
A new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed. Under the considerations of fuzzy parameters and fuzzy arithmetic operations (fuzzy addition and multiplication), we propose a fuzzy linear regression model which has the similar form as that of conventional one. We conduct the h-level (conventional) linear regression models of fuzzy linear regression model for the sake of invoking the statistical techniques in (conventional) linear regression analysis for real-valued data. In order to determine the sign (nonnegativity or nonpositivity) of fuzzy parameters, we perform the statistical testing hypotheses and evaluate the confidence intervals. Using the least squares estimators obtained from the h-level linear regression models, we can construct the membership functions of fuzzy least squares estimators via the form of “Resolution Identity” which is well-known in fuzzy sets theory. In order to obtain the membership degree of any given estimate taken from the fuzzy least squares estimator, optimization problems have to be solved. We also provide two computational procedures to deal with those optimization problems.
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Fuzzy prediction based on regression models

Abstract

Inform. Sci.

Inform. Sci.

Fuzzy Sets and Systems

Forecasting Methods and Applications

Econometric Models and Economic Forecasts

The concept of a linguistic variable and its application to approximate reasoning III

Inform. Sci.