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