Design of a multi-level fuzzy linear regression model for forecasting: A case study of Iran

Abstract

Linear regression has been widely used for many years to forecast various socio-economic variables in marketing, management, sales, energy and so on. Demand and price are commonly estimated by means of regression models. However, where there is high uncertainty in the model, fuzzy regressions are applied. In this paper, a fuzzy-based approach is applied for transport energy demand forecasting using socio-economic and transport related indicators. The model is based on Gross Domestic Product (GDP), population and the number of vehicles as three inputs to the main model.  Energy data from 1993 to 2005 are used to estimate each of the three inputs. By three individual fuzzy linear regression (FLR) models, a multi-level FLR model is designed. The input variables are transport energy demand in the last year, the number of vehicles, population and ratio of GDP overpopulation. The output variable is energy demand of the transportation sector in Iran. The inputs to the ending level are obtained as outputs of the starting levels.  The estimation fuzzy problem for the model is formulated as a linear optimization problem. Comparison of the model predictions with data of the testing period shows validity of the proposed model. Furthermore, having obtained the fuzzy parameters, the transport energy demand is predicted for 2006 to 2020. It is noticeable that, without any price shock or efficiency improvement in the transportation sector, the energy consumption may reach to a threatening level of about 592 MBOE by 2020.   Key words: Forecasting, multi-level fuzzy linear regression, transport energy demand, case study.