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

  • A. AzadehEmail author
  • O. Seraj
  • M. Saberi


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.


Fuzzy regression Fuzzy mathematical programming Electricity consumption Analysis of variance Uncertainty Mean absolute percentage error Index of confidence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Azadeh A, Ghaderi SF, Anvari M, Saberi M (2007) Performance assessment of electric power generations using an adaptive neural network algorithm. Energy Policy 35:3155–3166CrossRefGoogle Scholar
  2. 2.
    Azadeh A, Ghaderi SF, Tarverdian S, Saberi M (2007) Integration of artificial neural networks and genetic algorithm to predict electrical energy consumption. Appl Math Comput 186:1731–1741MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Azadeh A, Ghaderi SF, Sohrabkhani S (2007) Forecasting electrical consumption by integration of neural network, time series and ANOVA. Appl Math Comput 186:1753–1761MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Azadeh A, Tarverdian S (2007) Integration of genetic algorithm, computer simulation and design of experiment for forecasting electrical consumption. Energy Policy 35(10):5229–5241CrossRefGoogle Scholar
  5. 5.
    Azadeh A, Ghaderi SF, Anvari M, Saberi M (2006a) Measuring performance electric power generations using artificial neural networks and fuzzy clustering. In: Capolino GA, Franquelo LG (eds) Proceedings of the 32nd annual conference of the IEEE Industrial Electronics Society, IECON, Paris, 2006Google Scholar
  6. 6.
    Azadeh A, Ghaderi SF, Anvari M, Saberi M, Izadbakhsh H (2006) An integrated artificial neural network and fuzzy clustering algorithm for performance assessment of decision making units. Appl Math Comput 187(2):584–599MathSciNetCrossRefGoogle Scholar
  7. 7.
    Azadeh A, Ghaderi SF, Tarverdian S, Saberi M (2006c) Integration of artificial neural networks and GA to predict electrical energy consumption. In: Capolino GA, Franquelo LG (eds) Proceedings of the 32nd annual conference of the IEEE Industrial Electronics Society–IECON’06, Conservatoire National des Arts & Metiers, Paris, 2006Google Scholar
  8. 8.
    Azadeh A, Ghaderi SF, Sohrabkhani S (2008) A simulated-based neural network algorithm for forecasting electrical energy consumption in Iran. Energy Policy 36(7):2637–2644CrossRefGoogle Scholar
  9. 9.
    Azadeh A, Saberi M, Gitiforouz A, Saberi Z (2009) A hybrid simulation-adaptive network based fuzzy inference system for improvement of electricity consumption estimation. Expert Syst Appl 36(8):11108–11117CrossRefGoogle Scholar
  10. 10.
    Azadeh A, Saberi M, Seraj O (2010) An integrated fuzzy regression algorithm for energy consumption estimation with non-stationary data: a case study of Iran. Energy 35(6):2351–2366CrossRefGoogle Scholar
  11. 11.
    Azadeh A, Saberi M, Ghaderi SF, Gitiforouz A, Ebrahimipour V (2008) Improved estimation of electricity demand function by integration of fuzzy system and data mining approach. Energy Convers Manage 49(8):2165–2177CrossRefGoogle Scholar
  12. 12.
    Celmins A (1987) Least squares model fitting to fuzzy vector data. Fuzzy Sets Syst 22:245–269MathSciNetCrossRefGoogle Scholar
  13. 13.
    Celmins A (1987) Multidimensional least-squares model fitting of fuzzy models. Math Comput Model 9:669–690zbMATHGoogle Scholar
  14. 14.
    Chang PT, Lee ES (1996) A generalized fuzzy weighted least-squares regression. Fuzzy Sets Syst 82:289–298MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Chang YHO, Ayyub BM (2001) Fuzzy regression methods—a comparative assessment. Fuzzy Sets Syst 119:187–203MathSciNetCrossRefGoogle Scholar
  16. 16.
    Chen K, Rys MJ, Lee ES (2006) Modeling of thermal comfort in air conditioned rooms by fuzzy regression analysis. Math Comput Model 43:809–819zbMATHCrossRefGoogle Scholar
  17. 17.
    Chan KY, Kwong CK, Fogarty TC (2010) Modeling manufacturing processes using a genetic programming-based fuzzy regression with detection of outliers. Inf Sci 180(4):506–518CrossRefGoogle Scholar
  18. 18.
    Chen LH, Hsueh CC (2009) Fuzzy regression models using the least-squares method based on the concept of distance. IEEE Trans Fuzzy Syst 17(6):1259–1272CrossRefGoogle Scholar
  19. 19.
    Chen CW, Wang MHL, Lin JW (2009) Managing target cash balance in construction firms using fuzzy regression approach. Int J Uncertain Fuzziness Knowl-based Syst 17(5):667–684CrossRefGoogle Scholar
  20. 20.
    Diamond P (1988) Fuzzy least squares. Inf Sci 46:141–157MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    D’Urso P, Gastaldi T (2000) A least-squares approach to fuzzy linear regression analysis. Comput Stat Data Anal 34:427–440zbMATHCrossRefGoogle Scholar
  22. 22.
    Hojati M, Bector CR, Smimou K (2005) A simple method for computation of fuzzy linear regression. Eur J Oper Res 166:172–184MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Lai YJ, Chang SI (1994) A fuzzy approach for multi-response optimization: an off-line quality engineering problem. Fuzzy Sets Syst 63:117–129CrossRefGoogle Scholar
  24. 24.
    Modarres M, Nasrabadi MM, Nasrabadi E, Mohtashmi GR (2003) Evaluation of fuzzy linear regression models: a mathematical programming approach. In: Proceedings of 4th seminar on fuzzy sets and its applications, Babolsar, pp 129–135.Google Scholar
  25. 25.
    Nather W (1997) Linear statistical inference for random fuzzy data. Statistics 29:221–240MathSciNetCrossRefGoogle Scholar
  26. 26.
    Nather W, Albrecht M (1990) Linear regression with random fuzzy observations. Statistics 21:521–531MathSciNetCrossRefGoogle Scholar
  27. 27.
    Nather W (2000) On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data. Metrika 51:201–221MathSciNetCrossRefGoogle Scholar
  28. 28.
    Nasrabadi MM, Nasrabadi E, Nasrabadi AR (2005) Fuzzy linear regression analysis: a multi-objective programming approach. Appl Math Comput 163:245–251MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Ozelkan EC, Duckstein L (2000) Multi-objective fuzzy regression: a general framework. Comput Oper Res 27:635–652CrossRefGoogle Scholar
  30. 30.
    Peters G (1994) Fuzzy linear regression with fuzzy intervals. Fuzzy Sets Syst 63:45–55CrossRefGoogle Scholar
  31. 31.
    Ross TJ (1995) Fuzzy logic with engineering applications. McGraw-Hill, New YorkzbMATHGoogle Scholar
  32. 32.
    Sakawa M, Yano H (1992) Multi-objective fuzzy linear regression analysis for fuzzy input-output data. Fuzzy Sets Syst 47:173–181zbMATHCrossRefGoogle Scholar
  33. 33.
    Savic D, Pedrycz W (1991) Evaluation of fuzzy regression models. Fuzzy Sets Syst 39:51–63MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Tanaka H, Hayashi I, Watada J (1989) Possibilistic linear regression analysis for fuzzy data. Eur J Oper Res 40:389–396MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Tanaka H, Watada J (1988) Possibilistic linear systems and their application to the linear regression model. Fuzzy Sets Syst 27:275–289MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Tanaka H, Uejima S, Asia K (1982) Linear regression analysis with fuzzy model. IEEE Trans Syst Man Cybern 12:903–907zbMATHCrossRefGoogle Scholar
  37. 37.
    Wang HF, Tsaur RC (2000a) Resolution of fuzzy regression model. Eur J Oper Res 126:637–650MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Wang HF, Tsaur RC (2000b) Insight of a fuzzy regression model. Fuzzy Sets Syst 112:355–369MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Wu HC (2003) Fuzzy estimates of regression parameters in linear regression models for imprecise input and output data. Comput Stat Data Anal 42:203–217zbMATHCrossRefGoogle Scholar
  40. 40.
    Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning I, II and III. Inf Sci 8:199–249, 8, 301–357 and 9, 43–80MathSciNetCrossRefGoogle Scholar
  41. 41.
    Zeleny M (1982) Multiple criteria decision making. McGraw-Hill, New YorkzbMATHGoogle Scholar
  42. 42.
    Zhang GP (2001) An investigation of neural networks for linear time-series forecasting. Comput Oper Res 28:1183–1202zbMATHCrossRefGoogle Scholar
  43. 43.
    Narayan PK, Narayan S, Prasad A (2008) A structural VAR analysis of electricity consumption and real GDP: Evidence from the G7 countries. Energy Policy 36:2765–2769CrossRefGoogle Scholar
  44. 44.
    Amarawickrama HA, Hunt LC (2008) Electricity demand for Sri Lanka: a time series analysis. Energy 33:724–739CrossRefGoogle Scholar
  45. 45.
    Kulshreshtha M, Parikh JK (2000) Modelling demand for coal in India: vector autoregressive models with cointegrated variables. Energy 25:149–168CrossRefGoogle Scholar
  46. 46.
    Erzgräber H, Strozzi F, Zaldívar JM, Touchette H, Gutiérrez E, Arrowsmith DK (2008) Time series analysis and long range correlations of Nordic spot electricity market data. Physica A 387:6567–6574CrossRefGoogle Scholar
  47. 47.
    Uri ND (1978) Forecasting peak system load using a combined time series and econometric model. Appl Energy 4:219–227CrossRefGoogle Scholar
  48. 48.
    Rao RD, Parikh JK (1996) Forecast and analysis of demand for petroleum products in India. Energy Policy 24:583–592CrossRefGoogle Scholar
  49. 49.
    Gonzales Chavez S, Xiberta Bernat J, Llaneza Coalla H (1999) Forecasting of energy production and consumption in Asturias (Northern Spain). Energy 24:183–198CrossRefGoogle Scholar
  50. 50.
    Sfetsos A (2000) A comparison of various forecasting techniques applied to mean hourly wind speed time series. Renew Energy 21:23–35CrossRefGoogle Scholar
  51. 51.
    Sfetses A (2002) A novel approaches for the forecasting of mean hourly wind speed time series. Renew Energy 27:163–174CrossRefGoogle Scholar
  52. 52.
    Poggi P, Muselli M, Notton G, Cristofari C, Louche A (2003) Forecasting and simulating wind speed in Corsica by using an autoregressive model. Energy Convers Manage 44:3177–3196CrossRefGoogle Scholar
  53. 53.
    Körner R, Näther W (1998) Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least-squares estimates. Inform Sci, 109, pp 95–118.Google Scholar
  54. 54.
    Özelkan EC (1997) Multi-objective Fuzzy Regression Applied to the Calibration of Conceptual Rainfall–Runoff Models, Unpublished PhD Dissertation, Department of Systems and Industrial Engineering, The University of Arizona.Google Scholar
  55. 55.
    Özelkan EC, Duckstein L (2000) Multiobjective fuzzy regression: a general framework. Computers and Operation Research 27, pp 635–640.Google Scholar
  56. 56.
    Weron R, Misiorek A (2008) Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models. International Journal of Forecasting 24(4):744–763Google Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Center of Excellence for Intelligent-Based Experimental Mechanics, College of EngineeringUniversity of TehranTehranIran
  2. 2.Department of Industrial EngineeringUniversity of TafreshTafreshIran
  3. 3.Institute for Digital Ecosystems and Business IntelligenceCurtin University of TechnologyPerthAustralia

Personalised recommendations