An integrated fuzzy regression–analysis of variance algorithm for improvement of electricity consumption estimation in uncertain environments

This study presents an integrated fuzzy regression–analysis of variance (ANOVA) algorithm to estimate and predict electricity consumption in uncertain environment. The proposed algorithm is composed of 16 fuzzy regression models. This is because there is no clear cut as to which of the recent fuzzy regression model is suitable for a given set of actual data with respect to electricity consumption. Furthermore, it is difficult to model uncertain behavior of electricity consumption with conventional time series and proper fuzzy regression could be an ideal substitute for such cases. The algorithm selects the best model by mean absolute percentage error (MAPE), index of confidence (IC), distance measure, and ANOVA for electricity estimation and prediction. Monthly electricity consumption of Iran from 1992 to 2004 is considered to show the applicability and superiority of the proposed algorithm. The unique features of this study are threefold. The proposed algorithm selects the best fuzzy regression model for a given set of uncertain data by standard and proven methods. The selection process is based on MAPE, IC, distance to ideal point, and ANOVA. In contrast to previous studies, this study presents an integrated approach because it considers the most important fuzzy regression approaches, MAPE, IC, distance measure, and ANOVA for selection of the preferred model for the given data. Moreover, it always guarantees the preferred solution through its integrated mechanism.

[1]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[2]  Noel D. Uri,et al.  Forecasting peak system load using a combined time series and econometric model , 1978 .

[3]  A. Celmins.  Least squares model fitting to fuzzy vector data , 1987 .

[4]  A. Celmins.  Multidimensional least-squares fitting of fuzzy models , 1987 .

[5]  J. Watada,et al.  Possibilistic linear systems and their application to the linear regression model , 1988 .

[6]  Phil Diamond,et al.  Fuzzy least squares , 1988, Inf. Sci..

[7]  Junzo Watada,et al.  Possibilistic linear regression analysis for fuzzy data , 1989 .

[8]  Wolfgang Näther,et al.  Linear regression with random fuzzy observations , 1990 .

[9]  Witold Pedrycz,et al.  Evaluation of fuzzy linear regression models , 1991 .

[10]  Masatoshi Sakawa,et al.  Multiobjective fuzzy linear regression analysis for fuzzy input-output data , 1992 .

[11]  T. Ross.  Fuzzy Logic with Engineering Applications , 1994 .

[12]  Shing I. Chang,et al.  A fuzzy approach for multiresponse optimization: An off-line quality engineering problem , 1994 .

[13]  Georg Peters.  Fuzzy linear regression with fuzzy intervals , 1994 .

[14]  Jyoti K. Parikh,et al.  Forecast and analysis of demand for petroleum products in India , 1996 .

[15]  Ping-Teng Chang,et al.  A generalized fuzzy weighted least-squares regression , 1996, Fuzzy Sets Syst..

[16]  Wolfgang Näther.  Linear Statistical Inference for Random Fuzzy Data , 1997 .

[17]  Ertunga Cem Ozelkan.  Multi-objective fuzzy regression applied to the calibration of conceptual rainfall-runoff models , 1997 .

[18]  Wolfgang Näther,et al.  Linear Regression with Random Fuzzy Variables: Extended Classical Estimates, Best Linear Estimates, Least Squares Estimates , 1998, Inf. Sci..

[19]  S Gonzales Chavez,et al.  Forecasting of energy production and consumption in Asturias (northern Spain) , 1999 .

[20]  Hsiao-Fan Wang,et al.  Insight of a fuzzy regression model , 2000, Fuzzy Sets Syst..

[21]  W. Näther.  On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data , 2000 .

[22]  Pierpaolo D'Urso,et al.  A least-squares approach to fuzzy linear regression analysis , 2000 .

[23]  Lucien Duckstein,et al.  Multi-objective fuzzy regression: a general framework , 2000, Comput. Oper. Res..

[24]  Jyoti K. Parikh,et al.  Modeling demand for coal in India: vector autoregressive models with cointegrated variables , 2000 .

[25]  Hsiao-Fan Wang,et al.  Resolution of fuzzy regression model , 2000, Eur. J. Oper. Res..

[26]  Athanasios Sfetsos,et al.  A comparison of various forecasting techniques applied to mean hourly wind speed time series , 2000 .

[27]  Guoqiang Peter Zhang,et al.  An investigation of neural networks for linear time-series forecasting , 2001, Comput. Oper. Res..

[28]  Bilal M. Ayyub,et al.  Fuzzy regression methods - a comparative assessment , 2001, Fuzzy Sets Syst..

[29]  Athanasios Sfetsos,et al.  A novel approach for the forecasting of mean hourly wind speed time series , 2002 .

[30]  A. Louche,et al.  Forecasting and simulating wind speed in Corsica by using an autoregressive model , 2003 .

[31]  Hsien-Chung Wu,et al.  Fuzzy estimates of regression parameters in linear regression models for imprecise input and output data , 2003, Comput. Stat. Data Anal..

[32]  C. R. Bector,et al.  A simple method for computation of fuzzy linear regression , 2005, Eur. J. Oper. Res..

[33]  Ebrahim Nasrabadi,et al.  Fuzzy linear regression analysis: a multi-objective programming approach , 2005, Appl. Math. Comput..

[34]  M. Saberi,et al.  Improved Estimation of Electricity Demand Function by Integration of Fuzzy System and Data Mining Approach , 2006, 2006 IEEE International Conference on Industrial Technology.

[35]  M. Saberi,et al.  Measuring Performance Electric Power Generations Using Artificial Neural Networks and Fuzzy Clustering , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

[36]  S. F. Ghaderi,et al.  Integration of Artificial Neural Networks and Genetic Algorithm to Predict Electrical Energy consumption , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

[37]  E. Stanley Lee,et al.  Modeling of thermal comfort in air conditioned rooms by fuzzy regression analysis , 2006, Math. Comput. Model..

[38]  Seyed Farid Ghaderi,et al.  An integrated artificial neural network and fuzzy clustering algorithm for performance assessment of decision making units , 2007, Appl. Math. Comput..

[39]  Ali Azadeh,et al.  INTEGRATION OF GENETIC ALGORITHM, COMPUTER SIMULATION AND DESIGN OF EXPERIMENTS FOR FORECASTING ELECTRICAL ENERGY CONSUMPTION , 2007 .

[40]  Ali Azadeh,et al.  Forecasting electrical consumption by integration of Neural Network, time series and ANOVA , 2007, Appl. Math. Comput..

[41]  Ali Azadeh,et al.  Performance assessment of electric power generations using an adaptive neural network algorithm , 2007 .

[42]  H. Touchette,et al.  Time series analysis and long range correlations of Nordic spot electricity market data , 2008 .

[43]  Lester C. Hunt,et al.  Electricity demand for Sri Lanka : A time series analysis , 2008 .

[44]  Ali Azadeh,et al.  A simulated-based neural network algorithm for forecasting electrical energy consumption in Iran , 2008 .

[45]  R. Weron,et al.  Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models , 2008 .

[46]  Arti Prasad,et al.  A structural VAR analysis of electricity consumption and real GDP: Evidence from the G7 countries , 2008 .

[47]  Ali Azadeh,et al.  A hybrid simulation-adaptive network based fuzzy inference system for improvement of electricity consumption estimation , 2009, Expert Syst. Appl..

[48]  Jeng-Wen Lin,et al.  Managing Target the Cash Balance in Construction Firms Using a Fuzzy Regression Approach , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[49]  Liang-Hsuan Chen,et al.  Fuzzy Regression Models Using the Least-Squares Method Based on the Concept of Distance , 2009, IEEE Transactions on Fuzzy Systems.

[50]  Ali Azadeh,et al.  An integrated fuzzy regression algorithm for energy consumption estimation with non-stationary data: A case study of Iran , 2010 .

[51]  Kit Yan Chan,et al.  Modeling manufacturing processes using a genetic programming-based fuzzy regression with detection of outliers , 2010, Inf. Sci..

[52]  H. L. Gray,et al.  Applied time series analysis , 2011 .