Achieving greater Explanatory Power and Forecasting Accuracy with Non-uniform spread Fuzzy Linear Regression

TL;DR

This paper introduces a three-phase fuzzy linear regression model with non-uniform spreads, enhancing explanatory power and forecast accuracy by preserving fuzziness and accurately modeling spread variations.

Contribution

It presents a novel three-phase approach to construct fuzzy regression models with non-uniform spreads, improving upon previous methods that only addressed uniform spreads.

Findings

Demonstrates higher explanatory power in simulations

Achieves better forecasting accuracy

Effectively models non-uniform spreads in data

Abstract

Fuzzy regression models have been applied to several Operations Research applications viz., forecasting and prediction. Earlier works on fuzzy regression analysis obtain crisp regression coefficients for eliminating the problem of increasing spreads for the estimated fuzzy responses as the magnitude of the independent variable increases. But they cannot deal with the problem of non-uniform spreads. In this work, a three-phase approach is discussed to construct the fuzzy regression model with non-uniform spreads to deal with this problem. The first phase constructs the membership functions of the least-squares estimates of regression coefficients based on extension principle to completely conserve the fuzziness of observations. They are then defuzzified by the centre of area method to obtain crisp regression coefficients in the second phase. Finally, the error terms of the method are determined by setting each estimated spread equal to its corresponding observed spread. The Tagaki-Sugeno inference system is used for improving the accuracy of forecasts. The simulation example demonstrates the strength of fuzzy linear regression model in terms of higher explanatory power and forecasting performance.