Type 1 fuzzy function approach based on ridge regression for forecasting

Fuzzy function approach is a kind of fuzzy inference system that can produce successful results for the analysis of forecasting problems. In a fuzzy function approach, a fuzzy function corresponding to each fuzzy set is generated using multiple regression analysis. The number of explanatory variables in multiple regression analysis is increased via the non-linear transformations of the membership functions to improve the prediction performance of the model. In a fuzzy function approach, it can be found a high correlation between the non-linear transformations of membership functions, and therefore, the multiple linear regression method used to define fuzzy functions which has multicollinearity problem. The contribution of this paper is to propose a new fuzzy forecasting method to overcome this problem. In this paper, a new fuzzy function approach using ridge regression instead of multiple linear regression in Type 1 fuzzy function approach is proposed. The proposed new Type 1 approach is applied to various real world time series data and the results are compared to the ones obtained from other techniques. Thus, it is concluded that the results present superior forecasts performance.