A hybrid fuzzy mathematical programming-design of experiment framework for improvement of energy consumption estimation with small data sets and uncertainty: The cases of USA, Canada, Singapore, Pakistan and Iran

Utilization of small data sets for energy consumption forecasting is a major problem because it could create large noise. This study presents a hybrid framework for improvement of energy consumption estimation with small data sets. The framework is based on fuzzy regression, conventional regression and design of experiment (DOE). The hybrid framework uses analysis of variance (ANOVA) and minimum absolute percentage error (MAPE) to select between fuzzy and conventional regressions. The significance of the proposed framework is three fold. First, it is flexible and identifies the best model based on the results of ANOVA and MAPE. Second, the framework may identify conventional regression as the best model for future energy consumption forecasting because of its dynamic structure, whereas in the case of uncertainty and ambiguity, previous studies assume that fuzzy regression provides better solutions and estimation. Third, it is ideal candidate for short data sets. To show the applicability of the hybrid framework, the data for energy consumption in Canada, United States, Singapore, Pakistan and Iran from 1995 to 2005 are considered and tested. This is the first study which introduces a hybrid fuzzy regression-design of experiment for improvement of energy consumption estimation and forecasting with relatively small data sets.