基于智能方法的电力系统负荷预测模型及其应用研究
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摘要
电力系统负荷预测是能量管理系统和配电管理系统的重要部分,是实现自动发电控制和经济调度控制的前提,它涉及电力系统规划与设计,电力系统运行的经济性、安全性、可靠性和稳定性等。随着电力系统的不断发展和电网管理的日趋现代化、复杂化,电力系统负荷预测问题的研究引起人们广泛的关注。准确的电力负荷预测可以合理地安排电网内部发电机组的运行,保持电网运行的安全稳定性；可以合理的安排机组检修计划,保证社会的正常生产和人民的正常生活；可以决定新装机容量的大小与电网的调度控制,有效的降低发电成本,提高经济效益和社会效益。因此,电力系统负荷预测成为现代电力系统运行和管理中的一个重要研究课题和现代电力系统科学中的一个重要领域。
本文主要利用模糊数学、模糊时间序列、灰色系统理论、模糊多目标最优规划等智能方法,对电力系统负荷预测的模型与算法进行了应用研究。首先给出了基于模糊时间序列的基本预测模型与算法,并考虑到负荷自身变化的特点以及温度等综合因素对电力负荷的影响,对该预测模型进行了优化修正；其次基于稳健统计理论和模糊回归的思想,研究了稳健回归预测算法和稳健模糊回归预测算法；第三在离散灰色预测模型的基础上结合模糊多目标规划理论,研究了模糊离散灰色区间预测模型与算法；最后利用遗传算法和Pareto最优化理论来搜索和确定参数的最优区间,给出了基于多目标优化的模糊时间预测算法。针对不同的模型和算法,通过具体算例对不同预测模型与算法的预测结果进行了分析比较。论文的主要研究内容和创新点如下：
(1)基于模糊时间序列的预测模型与算法研究。在模糊时间序列基本理论框架下,将模糊时间序列预测模型应用到电力系统负荷预测中来。首先对历史负荷数据进行必要的预处理,以检测和平滑异常数据,其次考虑到电力负荷自身的特征以及影响负荷预测的重要因素,分别引入温度影响因子、负荷变化影响因子及综合影响因素作为权重因子,提出了时变-模糊时间序列预测算法和基于最高温度修正的最大负荷预测算法。最后通过两个数值算例,说明了我们提出的考虑因素分析的模糊时间序列预测算法具有较高的预测精度和较大的有效性和普遍适应性。
(2)基于稳健模糊回归的预测模型与算法研究。利用稳健统计和模糊回归的基本理论,研究了基于稳健估计的稳健回归预测算法和基于Tanaka's体系下的稳健模糊回归预测模型。该稳健回归预测算法通过函数的选择以及反复迭代减弱异常数值对回归方程的不利影响,增强回归方程的稳健性；而稳健模糊回归预测模型,借助于误差评价指标以及Tanaka's的模糊回归方法,研究并提出了一稳健模糊回归预测模型来预测模糊区间,通过一系列参数的优化和转化得到非线性模型。最后的两个算例,通过与传统算法和模型的比较,可以明显看出,我们提出的稳健算法和稳健模糊模型都能够有效降低异常数据对预测结果的影响,并且具有较好的稳定性。
(3)基于模糊离散灰色理论的区间预测模型研究。在离散灰色预测模型的基础上,结合模糊多目标最优化理论,研究并提出了基于离散灰色模型的模糊多目标区间预测模型。针对输入变量是精确数和模糊数,分别给出了不同的区间预测算法。并将本文的预测结果和现有文献中的模糊线性回归区间预测、灰色模糊区间预测结果进行比较,精确度更高；最后将该模型和算法应用于电力系统负荷区间预测,得到了更一般的预测结果,说明我们提出的模型和算法具有较广泛的适应性。
(4)基于多目标优化的模糊时间序列预测模型与算法研究。针对预测区间的划分是影响模糊时间序列预测精度的主要因素之一,首先定义和划分带有参数的预测区间,利用遗传算法搜索最优预测区间的长度并进行最优化参数的筛选和初始参数的选择,并借助于Pareto最优化理论识别最优解,提出了时变-基于比率的多目标最优化模糊时间序列预测模型和时不变-多目标最优化模糊时间序列预测模型,并将该模型和算法分别应用于Alabama大学入学率的预测,同已有文献相比,得到了较好的预测结果。最后,将我们提出的预测模型和算法应用于上海市用电量的长期预测,得到了更一般的预测结果,说明我们提出的预测模型和算法的有效性和适应性。
Electric load forecasting is one of the important parts in EMS and SMS and the precondition of the auto-generate electricity control and the economically attemper. It connected the programming and the design of the power system with the economical, security, reliability and stability. With the development of the electric power system and the management of electric grid becoming more and more modern and complexity, more and more researchers pay widely attention to the load forecasting problem. The accurate load forecasting could design the generator groups operational normally, keep up with security and stability of the electric power grid. Preparing the examination and reparation of the generator groups to be ensure the normal production and living; and effectively reducing the cost of generating electricity and enhancing the benefits of the societal and economic. So, the electric load forecasting is an important research topic and research field in modern power system operating and the management
In this thesis, the electricity load forecasting models and algorithms are discussed mainly using fuzzy mathematics, fuzzy time series theory, grey systems theory and fuzzy multi-objective programming etc the mathematics theory and intelligent method. Firstly, the basic fuzzy time series forecasting models and algorithms are given, Considering the changes of loads itself and temperature et al synthetical factors which affects on the loads, the optimal revised forecasting algorithm are studied again; secondly, a robust regression forecasting algorithm and robust fuzzy regression forecasting algorithm are discussed based on robust statistic theory and fuzzy regression theory, then, discrete grey interval forecasting models and algorithms are obtained based on the discrete grey forecasting model combined with fuzzy multi-objective theory, and at last, the fuzzy time series forecasting algorithm based on genetic algorithm to searching for the optimal parameters and Pareto optimization theory to determined the optimal interval are investigated. Considering the different forecasting models and algorithms, the numerical examples are given to comparing the forecasting results. The main research contents and innovative points are the follows:
(1) Research about electricity load forecasting algorithm based on fuzzy time series.
Based on the fuzzy time series theory, this paper introduce the fuzzy time series forecasting model and algorithm into the electric power system load forecasting. Firstly, the history loads are pre-disposed to recognize and smooth the outlier. then considering the characters of the loads and the important factors which affect on the load forecasting, the temperature influencing factor, the load changeable factor and the synthetical factors etc are introduced as the weight factors. So the time-variant fuzzy time series forecasting algorithm and maximum load forecasting algorithm based on bi-factor revised fuzzy time series model are proposed. At last, two numerical examples are given to validate our proposed forecasting model and algorithm have better forecasting effects and have an universality.
(2) Forecasting model and algorithm research based on robust fuzzy regression.
Based on robust statistic theory and Tanaka's fuzzy regression principle, a robust regression forecasting algorithm and a robust fuzzy regression forecasting model are studied. By considering the choice of the objective function and the weight function and the iterative procedure, The robust regression forecasting algorithm weakens the bad influence of the outlier to the regression equation and strengthens the robustness of the regression equation. On the other hands, the robust fuzzy regression forecasting model is studied, which gives the robust fuzzy forecasting interval by means of the error evaluative index and the Tanaka's fuzzy regression method. The nonlinear forecasting model is obtained by the optimization and the transform of the parameter. At last, the two numerical examples are given to compare the forecasting accuracy our proposed robust forecasting model and algorithm with the traditional forecasting method, and obviously, our proposed forecasting method could reduce the bad influence which the outlier made to the forecasting effects and could have a better robustness compared with the conventional methods.
(3) Research about fuzzy discrete gray interval forecasting model.
Based on discrete grey forecasting model combined with fuzzy multi-objective optimization theory, the fuzzy multi-objective discrete grey forecasting model is proposed. Considering the input variables are crisp data or the fuzzy data, the different interval forecasting model and algorithm are obtained.The forecasting results using our proposed forecasting model have a better accuracy compared with the forecasting results of the fuzzy linear regression interval forecasting and the grey fuzzy interval forecasting. Finally, we applied the forecasting model into the power system load interval forecasting and obtain the general results which illuminate that our proposed forecasting model have a universal and extensive applications.
(4) Research about the fuzzy time series forecasting model and algorithms based on Multi-objective optimization theory.
Because of the forecasting interval partitions is one of the important influence factors which affect the precision of the fuzzy time series forecasting, we first define and partition the forecasting interval with parameters, then using the genetic algorithm to searching for the optimal lengths of forecasting interval with parameters and Pareto optimization theory to identify the optimal solution and choice the initialization parameter. a time-variant ratio-multi objective optimal fuzzy time series forecasting model and a time-invariant multi-objective optimal fuzzy time series forecasting model and algorithms are proposed. When we apply our proposed forecasting model and algorithm to the enrollment forecasting of the Alabama, these forecasting results have a better forecasting precision compared with the other reference literatures. At last, we using our proposed two forecasting models and algorithms into the long term electricity consumption in shanghai and obtain the universal forecasting results which explain that our proposed forecasting methods have availability and applicability.
本文主要利用模糊数学、模糊时间序列、灰色系统理论、模糊多目标最优规划等智能方法,对电力系统负荷预测的模型与算法进行了应用研究。首先给出了基于模糊时间序列的基本预测模型与算法,并考虑到负荷自身变化的特点以及温度等综合因素对电力负荷的影响,对该预测模型进行了优化修正；其次基于稳健统计理论和模糊回归的思想,研究了稳健回归预测算法和稳健模糊回归预测算法；第三在离散灰色预测模型的基础上结合模糊多目标规划理论,研究了模糊离散灰色区间预测模型与算法；最后利用遗传算法和Pareto最优化理论来搜索和确定参数的最优区间,给出了基于多目标优化的模糊时间预测算法。针对不同的模型和算法,通过具体算例对不同预测模型与算法的预测结果进行了分析比较。论文的主要研究内容和创新点如下：
(1)基于模糊时间序列的预测模型与算法研究。在模糊时间序列基本理论框架下,将模糊时间序列预测模型应用到电力系统负荷预测中来。首先对历史负荷数据进行必要的预处理,以检测和平滑异常数据,其次考虑到电力负荷自身的特征以及影响负荷预测的重要因素,分别引入温度影响因子、负荷变化影响因子及综合影响因素作为权重因子,提出了时变-模糊时间序列预测算法和基于最高温度修正的最大负荷预测算法。最后通过两个数值算例,说明了我们提出的考虑因素分析的模糊时间序列预测算法具有较高的预测精度和较大的有效性和普遍适应性。
(2)基于稳健模糊回归的预测模型与算法研究。利用稳健统计和模糊回归的基本理论,研究了基于稳健估计的稳健回归预测算法和基于Tanaka's体系下的稳健模糊回归预测模型。该稳健回归预测算法通过函数的选择以及反复迭代减弱异常数值对回归方程的不利影响,增强回归方程的稳健性；而稳健模糊回归预测模型,借助于误差评价指标以及Tanaka's的模糊回归方法,研究并提出了一稳健模糊回归预测模型来预测模糊区间,通过一系列参数的优化和转化得到非线性模型。最后的两个算例,通过与传统算法和模型的比较,可以明显看出,我们提出的稳健算法和稳健模糊模型都能够有效降低异常数据对预测结果的影响,并且具有较好的稳定性。
(3)基于模糊离散灰色理论的区间预测模型研究。在离散灰色预测模型的基础上,结合模糊多目标最优化理论,研究并提出了基于离散灰色模型的模糊多目标区间预测模型。针对输入变量是精确数和模糊数,分别给出了不同的区间预测算法。并将本文的预测结果和现有文献中的模糊线性回归区间预测、灰色模糊区间预测结果进行比较,精确度更高；最后将该模型和算法应用于电力系统负荷区间预测,得到了更一般的预测结果,说明我们提出的模型和算法具有较广泛的适应性。
(4)基于多目标优化的模糊时间序列预测模型与算法研究。针对预测区间的划分是影响模糊时间序列预测精度的主要因素之一,首先定义和划分带有参数的预测区间,利用遗传算法搜索最优预测区间的长度并进行最优化参数的筛选和初始参数的选择,并借助于Pareto最优化理论识别最优解,提出了时变-基于比率的多目标最优化模糊时间序列预测模型和时不变-多目标最优化模糊时间序列预测模型,并将该模型和算法分别应用于Alabama大学入学率的预测,同已有文献相比,得到了较好的预测结果。最后,将我们提出的预测模型和算法应用于上海市用电量的长期预测,得到了更一般的预测结果,说明我们提出的预测模型和算法的有效性和适应性。
Electric load forecasting is one of the important parts in EMS and SMS and the precondition of the auto-generate electricity control and the economically attemper. It connected the programming and the design of the power system with the economical, security, reliability and stability. With the development of the electric power system and the management of electric grid becoming more and more modern and complexity, more and more researchers pay widely attention to the load forecasting problem. The accurate load forecasting could design the generator groups operational normally, keep up with security and stability of the electric power grid. Preparing the examination and reparation of the generator groups to be ensure the normal production and living; and effectively reducing the cost of generating electricity and enhancing the benefits of the societal and economic. So, the electric load forecasting is an important research topic and research field in modern power system operating and the management
In this thesis, the electricity load forecasting models and algorithms are discussed mainly using fuzzy mathematics, fuzzy time series theory, grey systems theory and fuzzy multi-objective programming etc the mathematics theory and intelligent method. Firstly, the basic fuzzy time series forecasting models and algorithms are given, Considering the changes of loads itself and temperature et al synthetical factors which affects on the loads, the optimal revised forecasting algorithm are studied again; secondly, a robust regression forecasting algorithm and robust fuzzy regression forecasting algorithm are discussed based on robust statistic theory and fuzzy regression theory, then, discrete grey interval forecasting models and algorithms are obtained based on the discrete grey forecasting model combined with fuzzy multi-objective theory, and at last, the fuzzy time series forecasting algorithm based on genetic algorithm to searching for the optimal parameters and Pareto optimization theory to determined the optimal interval are investigated. Considering the different forecasting models and algorithms, the numerical examples are given to comparing the forecasting results. The main research contents and innovative points are the follows:
(1) Research about electricity load forecasting algorithm based on fuzzy time series.
Based on the fuzzy time series theory, this paper introduce the fuzzy time series forecasting model and algorithm into the electric power system load forecasting. Firstly, the history loads are pre-disposed to recognize and smooth the outlier. then considering the characters of the loads and the important factors which affect on the load forecasting, the temperature influencing factor, the load changeable factor and the synthetical factors etc are introduced as the weight factors. So the time-variant fuzzy time series forecasting algorithm and maximum load forecasting algorithm based on bi-factor revised fuzzy time series model are proposed. At last, two numerical examples are given to validate our proposed forecasting model and algorithm have better forecasting effects and have an universality.
(2) Forecasting model and algorithm research based on robust fuzzy regression.
Based on robust statistic theory and Tanaka's fuzzy regression principle, a robust regression forecasting algorithm and a robust fuzzy regression forecasting model are studied. By considering the choice of the objective function and the weight function and the iterative procedure, The robust regression forecasting algorithm weakens the bad influence of the outlier to the regression equation and strengthens the robustness of the regression equation. On the other hands, the robust fuzzy regression forecasting model is studied, which gives the robust fuzzy forecasting interval by means of the error evaluative index and the Tanaka's fuzzy regression method. The nonlinear forecasting model is obtained by the optimization and the transform of the parameter. At last, the two numerical examples are given to compare the forecasting accuracy our proposed robust forecasting model and algorithm with the traditional forecasting method, and obviously, our proposed forecasting method could reduce the bad influence which the outlier made to the forecasting effects and could have a better robustness compared with the conventional methods.
(3) Research about fuzzy discrete gray interval forecasting model.
Based on discrete grey forecasting model combined with fuzzy multi-objective optimization theory, the fuzzy multi-objective discrete grey forecasting model is proposed. Considering the input variables are crisp data or the fuzzy data, the different interval forecasting model and algorithm are obtained.The forecasting results using our proposed forecasting model have a better accuracy compared with the forecasting results of the fuzzy linear regression interval forecasting and the grey fuzzy interval forecasting. Finally, we applied the forecasting model into the power system load interval forecasting and obtain the general results which illuminate that our proposed forecasting model have a universal and extensive applications.
(4) Research about the fuzzy time series forecasting model and algorithms based on Multi-objective optimization theory.
Because of the forecasting interval partitions is one of the important influence factors which affect the precision of the fuzzy time series forecasting, we first define and partition the forecasting interval with parameters, then using the genetic algorithm to searching for the optimal lengths of forecasting interval with parameters and Pareto optimization theory to identify the optimal solution and choice the initialization parameter. a time-variant ratio-multi objective optimal fuzzy time series forecasting model and a time-invariant multi-objective optimal fuzzy time series forecasting model and algorithms are proposed. When we apply our proposed forecasting model and algorithm to the enrollment forecasting of the Alabama, these forecasting results have a better forecasting precision compared with the other reference literatures. At last, we using our proposed two forecasting models and algorithms into the long term electricity consumption in shanghai and obtain the universal forecasting results which explain that our proposed forecasting methods have availability and applicability.
引文
[1]康重庆,夏清,徐玮.电力系统不确定性分析[M].北京：科学出版社,2011.
[2]牛东晓,曹树华,赵磊,等.电力负荷预测技术及其应用[M].北京：中国电力出版社,1998.
[3]赵希正.中国电力负荷特性分析与预测[M].北京：中国电力出版社,2002.
[4]鞠平.电力系统建模理论与方法[M].北京：科学出版社,2010.
[5]H.K.Alfares, M.Nazeeruddin. Electric load forecasting:literature survey and classification of methods[J]. International Journal of Systems Science, 2002,33:23-34.
[6]H.Hahn, S.M.Nieberg, S.Pickl. Electric load forecasting methods:tools for decision making[J]. European Journal of Operational Research, 2009,199(3):902-907.
[7]E.Almeshaiei, H.Saltan. A methodology for electric power load forecasting[J]. Alexandria Engineering Journal 2011,5:137-144.
[8]L.A.Zadeh. Fuzzy sets[J]. Information and Control,1965:338-353.
[9]L.A.Zadeh. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy Sets and Systems,1978:3-28.
[10]H.Tanaka, S.Uegima, K.Asai. Linear regression analysis with fuzzy model[J]. IEEE Transactions Systems Man Cybernet,1982,12:903-907.
[11]H.Tanaka. Fuzzy data analysis by possibilistic linear models[J]. Fuzzy Sets and Systems,1987,24:363-375.
[12]H.J.Zimmermann. Fuzzy Sets Theory and its Applications[M]. Kluwer, Boston, MA,1985.
[13]M.Hojati, C.R.Bector, K.Smimou. A simple method for computation of fuzzy linear regression [J]. European Journal of Operational Research, 2005,166:172-184.
[14]P. Diamond. Fuzzy least squares[J]. Information Sciences, 1998,46:141-157.
[15]C.L.Hor, S.J.Watson, S.Majithia. Analyzing the impact of weather variables on monthly electricity demands[J]. IEEE Transactions on Power Systems,2005,20 (4):2078-2085.
[16]M.Kelkinnama,S.M.Taheri. Fuzzy least-absolutes regression using shape preserving operations[J]. Information Sciences,2012,214:105-120.
[17]H.Shakouri, R.Nadimi. Outlier detection in fuzzy linear regression with crisp input-output by linguistic variable view[J]. Applied Soft Computing, 2013,13:734-742.
[18]T.Y.Chou, G.S.Liang, T.C.Han. Application of fuzzy regression on air cargo volume forecast[J]. Qual Quant,2013,47:897-908.
[19]G.E.P.Box, G.M.Jenkins. Time Series Analysis[M]. Forecasting and Control, Holden-Day, San Francisco,1970.
[20]D.Pfeffermann, J.Allon. Multivariate exponential smoothing:Methods and practice[J]. International Journal of Forecasting,1989,5:83-98.
[21]P.J.Brockwell,R.A.Davis.Time Series:Theory and Methods[M].2nd Springer-Verlag,1991.
[22]J.W.Taylor. Exponential smoothing with a damped multiplicative trend[J]. International Journal of Forecasting,2003,19:273-289.
[23]J.G.DeGooijer, R.J.Hyndman.25 years of time series forecasting[J]. International Journal of Forecasting,2006,22:443-473.
[24]Y.S.Lee, L.I.Tong. Forecasting nonlinear time series of energy consumption using a hybrid dynamic model[J]. Applied Energy,2012,94:251-256.
[25]M.Stepnicka, P.Cortez, J.P.Donate, L.Stepnickova. Forecasting seasonal time series with computational intelligence:On recent methods and the potential of their combinations[J]. Expert Systems with Applications,2013, 40:1981-1992.
[26]M.Bozic, M.Stojanovic, Z.Stajic, et al. Mutual Information-Based Inputs Selection for Electric Load Time Series Forecast ing [J]. Entropy,2013,15: 926-942.
[27]J.L.Deng. The Control problem of grey systems [J]. Systems&Control Letter,1982,1(5):288-294.
[28]S.F.Liu, YXin. Grey information[M]. New York:Springer,2006.
[29]L.F.Wu, S.F. Liu L.G..Yao,etal.Grey system model with the fractional order accumulation Commun Nonlinear Sci Numer Simulat,2013,18:1775-1785.
[30]L.F.Wu, S.F. Liu L.G..Yao,etal. The effect of sample size on the Grey system model[J]. Applied Mathematical Modelling,2013,37:6577-6583.
[31]C.C.Hsu, C.Y.Chen. Applications of improved Grey prediction model for power demand forecasting[J]. Energy Conversion and Management, 2003,44:2241-2249.
[32]焦润海,苏辰隽,林碧英等.基于气象信息因素修正的灰色短期负荷预测模型[J].电网技术,2013,37(3)：720-725.
[33]D.C.Park, M.A.El-SharKawi, R.J.Marks, etal. Electric load forecasting using a neural network[J].IEEE Transactions on Power Systems,1991,6(2): 442-449.
[34]H.S.Hippert, C.E.Pedreira, R.C.Souza. Neural networks for short-term load forecasting:A review and evaluation[J]. IEEE Transactions on Power Systems,2001,16(1):44-55.
[35]H.S.Hippert, D.W.Bunn, R.C.Souza. Large neural networks for electricity load forecasting:Are they overfitted[J]. International Journal of Forecasting, 2005,21:425-434.
[36]L.Hernandez, C.Baladr6n, J.M.Aguiar, et al. Short-Term Load Forecasting for Microgrids Based on Artificial Neural Networks[J]. Energies,2013,6: 1385-1408.
[37]U.Yolcu, E.Egrioglu, C.H.Aladag. A new linear & nonlinear artificial neural network model for time series forecasting[J]. Decision Support Systems, 2013,54:1340-1347.
[38]D.Singhal, K.S.Swarup. Electricity price forecasting using artificial neural networks[J]. Electrical Power and Energy Systems,2011,33:550-555.
[39]C.Hamzacebi. Improving artificial neural networks performance in seasonal time series forecasting[J]. Information Sciences,2008,178:4550-4559.
[40]S.C.Pandian, K.Duraiswamy, C.C.A.Rajan, N.Kanagaraj. Fuzzy approach for short term load forecasting[J]. Electric Power Systems Research, 2006,76:541-548.
[41]P.F.Pai. Hybrid ellipsoidal fuzzy systems in forecasting regional electricity loads[J]. Energy Conversion and Management,2006,47:2283-2289.
[42]L.C.Ying, M.C.Pan. Using adaptive network based fuzzy inference system to forecast regional electricity loads[J]. Energy Conversion and Management,2008,49:205-211.
[43]V.Vapnik. The Nature of Statistical Learning[M]. New York, Springer,1995.
[44]B.J.Chen, M.W.Chang, C.J.Lin. Load forecasting using support vector machines:A study on EUNITE competition[J]. IEEE Transactions on Power Systems,2001,19 (4):1821-1830.
[45]J.Wang, Y.Zhou, Y.Chen. Electricity load forecasting based on support vector machines and simulated annealing particle swarm optimization algorithm[C]. Proceedings of the IEEE International Conference on Automation and Logistics,2007:2836-2840.
[46]P.F.Pai, W.C.Hong. Forecasting regional electricity load based on recurrent support vector machines with genetic algorithms [J]. Electric Power Systems Research,2005,74(3):417-425.
[47]D.X.Niu, Y.L.Wang,D.D.Wu. Power load forecasting using support vector machine and ant colony optimization[J]. Expert Systems with Applications,2010,37(3):2531-2539.
[48]A. Miranian,M.Abdollahzade. Developing a Local Least-Squares Support Vector Machines-Based Neuro-Fuzzy Model for Nonlinear and Chaotic Time Series Prediction[J]. IEEE Transactions on Neural Networks and Learning Systems,2013,24(2):207-218.
[49]A. Mellit, A. Massi Pavan, M. Benghanem. Least squares support vector machine for short-term prediction of meteorological time series[J]. Theor Appl Climatol,2013,111:297-307.
[50]M.Alamaniotis, A.Ikonomopoulos, L.H.Tsoukalas. Evolutionary Multiobjective Optimization of Kernel-Based Very-Short-Term Load Forecasting[J]. IEEE Transactions on Power Systems,2012,27(3): 1477-1484.
[51]N. Amjady, A. Daraeepour. Midterm demand prediction of electrical power systems using a new hybrid forecasting technique[J].IEEE Transactions on Power Systems,2011,26(2):755-765.
[52]R.A.Hooshmand, H.Amooshahi, M.Parastegari. A hybrid intelligent algorithm based short-term load forecasting approach[J]. International Journal of Electrical Power & Energy Systems,2013,45(1):313-324.
[53]Q.Song, B.S.Chissom. Fuzzy time series and its models[J]. Fuzzy Sets System,1993,54:269-277.
[54]Q.Song, B.S.Chissom. Forecasting enrollments with fuzzy time series-Part 1[J]. Fuzzy Sets System,1993,54:1-9.
[55]Q.Song, B.S.Chissom. Forecasting enrollments with fuzzy time series-Part 2[J]. Fuzzy Sets System,1994,62:1-8.
[56]S.M.Chen. Forecasting enrollments based on fuzzy time series[J]. Fuzzy Sets System,1996,81:311-319.
[57]S.M.Chen. Forecasting enrollments based on high-order fuzzy time series[J]. Cybernetics and Systems:An International Journal,2002,33:1-16.
[58]S.M.Chen, J.R.Hwang. Temperature prediction using fuzzy time series[J]. IEEE Transactions System Man Cybernation. Part B,2000,30(2):263-275.
[59]S.M.Chen, N.Y.Chung. Forecasting enrollments using high-order fuzzy time series and genetic algorithms [J]. International Journal of Intelligent Systems,2006,21(5):485-501.
[60]S.M.Chen and N.Y.Chung. Forecasting enrollments of students by using fuzzy time series and genetic algorithms [J]. Information and Management Sciences,2006,17(3):1-17.
[61]K.H.Huarng. Effective lengths of intervals to improve forecasting in fuzzy time series[J]. Fuzzy Sets System,2001,123:387-394.
[62]K.H.Huarng,T.H.K.Yu. Ratio-based lengths of intervals to improve fuzzy time series forecasting[J]. IEEE Transactions System Man Cybernation, Part B,2006,36(2):328-340.
[63]K.H.Huarng, T.H.K.Yu. A multivariate heuristic model for fuzzy time-series forecasting[J]. IEEE Transaction System Man Cybernation, Part B,2007, 37(4):836-846.
[64]C.H.Cheng, R.J.Chang, C.A.Yeh. Entropy-based and trapezoidal fuzzification-based fuzzy time series approach for forecasting IT project cost[J]. Technological Forecasting and Social Change,2006,73(5): 524-542.
[65]C.H.Cheng, T.L.Chen, H.J.Teoh, C.H.Chiang. Fuzzy time-series based on adaptive expectation model for TAIEX forecasting[J]. Expert Systems with Applications,2008,34:1126-1132.
[66]C.H.Cheng, G.W.Cheng.J.W.Wang. Multi-attribute fuzzy time series method based on fuzzy clustering[J]. Expert Systems with Applications, 2008,34,1235-1242.
[67]S.T.Li, Y.C.Cheng, and S.Y.Lin. A FCM-based deterministic forecasting model for fuzzy time series[J]. Computers and Mathematics with Applications,2008,56(12):3052-3063.
[68]I.H.Kuo, S.J.Horng, T.W.Kao,et al. An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization [J]. Expert Systems with Applications,2009,36(3):6108-6117.
[69]R.C.Tsaur, J.C.O.Yang, and H.F.Wang. Fuzzy relation analysis in fuzzy time series model [J]. Computers and Mathematics with Applications,2005,49:539-548.
[70]L.W.Lee, L.H.Wang, S.M.Chen, et.al. Handling forecasting problems based on two-factors high-order fuzzy time series[J]. IEEE Transactions Fuzzy System,2006,14(3):468-477.
[71]C.H.Aladag, M.A.Basaran, E.Egrioglu, U.Yolcu, and V.R.Uslu. Forecasting in high order fuzzy time series by using neural networks to define fuzzy relations[J]. Expert Systems with Applications,2009,36(3):4228-4231.
[72]Y.Y.Hsu, S.M.Tse, B.Wu. A new approach of bivariate fuzzy time series analysis to the forecasting of a stock index[J]. Internal Journal Uncertainty Fuzziness Knowledge-Based System,2003,11(6):671-690.
[73]U.Yolcu, E.Egrioglu, V.R.Uslu, M.A.Basaran,C.H.Aladag. A new approach for determining the length of intervals for fuzzy time series[J]. Applied Soft Computing,2009,9:647-651.
[74]E.Egrioglu, C.H. Aladag, U.Yolcu, M.A.Basaran &, V.R.Uslu. A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model[J]. Expert Systems with Applications, 2009,36:7424-7434.
[75]E.Egrioglu, C.H. Aladag, U.Yolcu, V.R.Uslu & M.A.Basaran. A new approach based on artificial neural networks for high order multivariate fuzzy time series[J]. Expert Systems with Applications,2009,36: 10589-10594.
[76]E.Egrioglu, C.H. Aladag, U.Yolcu, V.R.Uslu & M.A.Basaran. Finding an optimal interval length in high order fuzzy time series [J]. Expert Systems with Applications,2010,37:5052-5055.
[77]E.Egrioglu, C.H. Aladag, M.A.Basaran, V.R.Uslu, V.R.Uslu. A new approach based on the optimization of the length of intervals in fuzzy time series[J]. Journal of Intelligent and Fuzzy Systems,2011,22:15-19,
[78]E.Egrioglu, C.H. Aladag, U.Yolcu, V.R.Uslu & N.A.Erilli.Fuzzy time series forecasting method based on Gustafson-Kessel fuzzy clustering[J]. Expert Systems with Applications,2011,38:10355-10357.
[79]E.Egrioglu, C.H.Aladag, U.Yolcu. Fuzzy time series forecasting with a novel hybrid approach combining fuzzy c-means and neural networks[J]. Expert Systems with Applications,2013,40:854-857.
[80]F.M.Tseng, G.H.Tzeng, H.C.Yu,et al. Fuzzy ARIMA model for forecasting the foreign exchange market[J]. Fuzzy Sets System,2001,18:9-19.
[81]J.R.Poulsen. Fuzzy Time Series Forecasting[D]. Aalborg University Esbjerg (AAUE),2009.
[82]H.Saima, JJafreezal, B.S.Brahim, A.J.Tahseen. A Hybrid Fuzzy Time Series Model for Forecasting[J]. Engineering Letters,2012:1-6.
[83]R. Mamlook, O. Badran and E. Abclulhadi. A fuzzy inference model for short term load forecasting [J]. Energy Policy,2009,37(4):1239-1248.
[84]H.T.Liu, N.C.Wei, C.G.Yang. Improved time-variant fuzzy time series Forecast[J]. Fuzzy Optimization Decision Making,2009,8(1):45-65.
[85]C.A.Maia, M.M.Goncalves. Application of switched adaptive system to load forecasting [J] Electric power systems research,2008,78(5):721-727.
[86]H.K.Yu. Weighted fuzzy time series models for TAIEX forecasting [J]. Physica A,2005,349:609-624.
[87]C.H.Cheng,T.L.Chen,C.H.Chian.Trend-weighted fuzzy time seride model for TAIEX Forecasting[C].Lecture Notes in Computer Science,2006, 4234:469-477.
[88]H.J.Teoh,T.L.Chen,C.H.Cheng. Frequency-weighted fuzzy time-series based on Fibonacci sequence for TAIEX forecasting[C]. Lecture Notes in Computer Science,2007,4819:27-34.
[89]W.K.Wong, E.J.Bai, W.C.Chu. Adaptive time-variant models for fuzzy time-series forecasting[J]. IEEE Transactions on Systems Man and Cybernetics-Part B:Cybernetics 2010,40(6):1531-1534.
[90]X.J.Liu, E.J.Bai, J.A.Fang and L.H.Luo. Time-Variant Slide Fuzzy Time-series Method for Short-Term Load Forecasting [C].2010 IEEE ICIS (Intelligent Computing and Intelligent Systems) 2010,1:65-68.
[91]刘晓娟,方建安.综合权重的模糊时间序列的电力负荷预测方法[J].华东电力,2012,40(4)：518-520.
[92]X.J.Liu, E.J.Bai, J.A.Fang. Weighted Time-variant Slide Fuzzy Time-series Models for Short-Term Load Forecasting[J]. Journal of Intelligent Learning Systems and Applications,2012,4:285-290.
[93]E.J.Bai, W.C.Chu, W.K.Wong, Xia M, Pan F. A heuristic time-invariant model for fuzzy time series forecasting [J]. Expert Systems with Applications,2011,38(3):2701-2707.
[94]姜学宝,吴强.苏州电网负荷和敏感性分析[J].江苏电机工程,2009,28(6)：45-48.
[95]D.T. Redden, W.H.Woodall. Properties of certain fuzzy linear regression methods[J]. Fuzzy Sets and Systems,1994,64(3):361-375.
[96]P.F.Christoffersen. Evaluating interval forecasts[J]. International Economic Review,1998,39(4):841-862.
[97]B.Kim, R.R.Bishu. Evaluation of fuzzy linear regression models by comparison membership function[J]. Fuzzy Sets and Systems,1998,100(1): 343-352.
[98]R.C.Tsaur, H.F.Wang, J.C.O.Yang. Fuzzy regression for seasonal time series analysis[J]. International Journal of Information Technology and Decision Making,2002,1(1):165-175.
[99]R.C.Tsaur. Forecasting analysis by using fuzzy grey regression model for solving limited time series data[J]. Soft Computing,2008,12:1105-1113.
[100]R.C.Tsaur. The development of an interval grey regression model for limited time series forecasting [J]. Expert Systems with Applications, 2010,37:1200-1206.
[101]J.R.Yu, G.H.Tzeng, H.L.Li. A general piecewise necessity regression analysis based on linear programming[J]. Fuzzy Sets and Systems, 1999,105(3):429-436.
[102]D.H.Hong, S.H.Lee, H.Y..Do, Fuzzy linear regression analysis for fuzzy input-output data using shape-preserving operations[J]. Fuzzy Set and Systems,2001,122:513-526.
[103]D.H.Hong, J.K.Song, H.Y.Do. Fuzzy least squares linear regression analysis using shape preserving operation [J].Information Sciences,2001, 138(1):185-193.
[104]M.S.Yang, T.S.Lin. Fuzzy least-squares linear regression analysis for fuzzy input-output data[J]. Fuzzy Sets and Systems,2002,126(3):389-399.
[105]M.S.Yang, H.H.Liu. Fuzzy least-squares algorithms for interactive fuzzy linear regression models[J]. Fuzzy Sets and Systems,2003,135(2): 305-316.
[106]K.B.Song, Y.S.Baek, D.H.Hong, etc. Short-Term Load Forecasting for the holidays using fuzzy linear regression method. Transactions on power systems 2005,20(1):96-101.
[107]S.H.Choi, J.J.Buckley. Fuzzy regression using least absolute deviation estimators[J].Soft Computing,2008,12:257-263.
[108]M.M.Nasrabadi, E.Nasrabadi. A mathematical programming approach to fuzzy linear regression analysis[J]. Applied Mathematics and Computation, 2004,155(3):873-881.
[109]M.M.Nasrabadi, E.Nasrabadi,A.R.Nasrabady. Fuzzy linear regression analysis:a multi-objective programming approach[J].Applied Mathematics and Computation,2005,163:245-251.
[110]黄华,宋艳萍,苗新艳等.基于多目标规划法的模糊线性回归分析[J].模糊系统与数学,2012,26(3)：114-119.
[111]M.Hojati, C.R.Bector, K.Smimou. A simple method for computation of fuzzy linear regression [J]. European Journal of Operational Research,2005,166:172-184.
[112]Q.Wu. Fuzzy fault diagnosis based on fuzzy robust v-support vector classifier and modified genetic algorithm [J]. Expert Systems with Applications,2011,38:4882-4888.
[113]Q.Wu. The complex fuzzy system forecasting model based on triangular fuzzy robust wavelet m-support vector machine[J]. Expert Systems with Applications,2011,38:14478-14489.
[114]A.Bolotin. Robustness of the regression models for uncertain categories [J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2007,15(6):681-695.
[115]H.C.Wu. Linear regression analysis for fuzzy input and output data using the extension principle [J].Computers Mathematics with Application,2003, 45(12):1849-1859.
[116]P.Durso,T.Gastaldi. A least-squares approach to fuzzy linear regression analysis[J]. Computation Statistics and Data Analysis,2000,34(4): 427-440.
[117]A.Bargiela,W.Pedrycz, T.Nakashima. Multiple regression with fuzzy data[J]. Fuzzy Sets and Systems,2007,158:2169-2188.
[118]A.Bisserier,R.Boukezzoula,S.Galichet. Linear fuzzy regression using trapezoidal fuzzy intervals [J]. Journal of Uncertain Systems,2010,4(1): 59-72.
[119]A.Bisserier, R.Boukezzoula, S.Galichet. A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals[J]. Information Sciences, 2010,180(19):3653-3673.
[120]E.Nasrabadi,S.M.Hashemi. Robust fuzzy regression analysis using neural networks[J]. International Journal Uncertainty, Fuzziness and Knowledge-Based Systems,2008,16:579-598.
[121]Y.L.Huang, C.T.Lin. Developing an interval forecasting method to predict undulated demand[J]. Qual Quant,2011,45(3):513-524.
[122]Y.M.Wi, S.K.Joo and K.B.Song. Holiday load forecasting using fuzzy polynomial regression with weather feature selection and adjustment[J]. IEEE Transactions on Power Systems,2012,27(2):596-603.
[123]H.Katagiri, T.Uno, K.Kato, etal. Random fuzzy multi-objective linear programming:Optimization of possibilistic value at risk (pVaR)[J].Expert Systems with Applications,2013,40:563-574.
[124]P.J.Rousseeuw, A.M.Leroy. Robust Regression&Outliers Detection[M]. John Wiley and Sons Inc., Hoboken, NJ,2001.
[125]P.D'Urso, R.Massari, A.Santoro. Robust fuzzy regression analysis[J]. Information Sciences,2011,181:4154-4174.
[126]T.D.Nguyen, R.Welsch. Outlier detection and least trimmed squares approximation using semi-definite programming[J]. Computational Statistics and Data Analysis,2010,54(12):3212-3226.
[127]K.Shibata, J.Watada, Y.Yabuuchi. A fuzzy regression approach for evaluating electric and electronics corporations[J]. Journal of Japan Industrial Management Associations,2008,59(1):58-67.
[128]S.Varga. Robust estimations in classical regression models versus robust estimations in fuzzy regression models[J]. Kybernetika,2007,43 (4):503-508.
[129]T.Torabi, J.Behboodian. Fuzzy least-absolutes estimates in linear models[J]. Communications in Statistics:Theory and Methods,2007,36 (10):1935-1944.
[130]B.Y. Sohn. Robust fuzzy linear regression based on M-estimators [J]. Journal of Application Mathematics and Computing,2005,18(1):591-601.
[131]M.C.Ortiz, L.A.Sarabia, A.Herrero. Robust regression techniques A useful alternative for the detection of outlier data in chemical analysis[J]. Talanta, 2006,70:499-512.
[132]Y.Chakhchoukh. A new robust estimation method for short-term load forecasting [C].17th European Signal Processing Conference, EUSIPCO 2009:2489-2493.
[133]Y.Chakhchoukh, P.Panciatici, L.Mili. Electric load forecasting based on statistical robust methods[J]. IEEE Transactions on Power Systems,2007, 6(1):1-12.
[134]Y.Chakhchoukh. A new robust estimation method for ARMA models[J]. IEEE Transactions on signal processing,2010,58(7):3512-3522.
[135]Z.M.Song, X.P.Xiao,J.L.Deng.The character of opposite direction AGO and class ratio[J].The Journal of Grey System,2002,14(1):9-14.
[136]D.Akay, M.Atak.Grey prediction with rolling mechanism for electricity demand forecasting of Turkey[J]. Energy,2007,32:1670-1675.
[137]Y.H.Lin, P.C.Lee. Novel high precision grey forecasting model[J], Automation in Construction,2007,16:771-777.
[138]Y.H.Lin, P.C.Lee, T.P.Chang. Adaptive and high-precision grey forecasting model[J]. Expert System and Applications,2009,36:9658-9662.
[139]Z.Zhao, J.Z.Wang,J.Zhao,et al. Using a grey model optimized by differential evolution algorithm to forecasting the per capita annual net income of rural households in china[J]. Omega,2012,40:525-532.
[140JN.M. Xie, S.F. Liu. Discrete grey forecasting model and its optimization[J]. Applied Mathematical Modeling,2009,33:1173-1186.
[141]N.M.Xie, S.F.Liu,Y.J.Yang,C.Q.Yuan. On novel grey forecasting model based on non-homogeneous index sequence[J]. Applied Mathematical Modeling,2013,37:5059-5068.
[142]T.X.Yao, S.F.Liu and N.M.Xie. On the properties of small sample of GM(1,1) model[J]. Applied Mathematical Modeling,2009,33:1894-1903.
[143]B.zeng, S.F.Liu and N.M.Xie. Prediction model of interval grey number based on DGM(1,1)[J]. Journal of Systems Engineering and Electronics, 2010,21(4):598-603.
[144]J.Cui, S.F.Liu, B.Zeng, N.M.Xie. A novel grey forecasting model and its optimization[J]. Applied Mathematical Modeling,2013,37:4399-4406.
[145]L.F.Wu, S.F.Liu,Y.N.Wang. Grey Lotka-Volterra model and its application[J]. Technological Forecasting & Social Change,2012,79: 1720-1730.
[146]L.F.Wu, S.F.Liu, L.G.Yao,S.L.Yan, D.L.Liu. Grey system model with the fractional order accumulation [J]. Communications in Nonlinear Science and Number Simulation,2013,18:1775-1785.
[147]E.Kayacan, B.Ulutas, O-Kaynak. Grey system theory-based models in time series prediction[J]. Expert Systems with Applications,2010,37: 1784-1789.
[148]S. J.Feng, YD.Ma, Z.L.Song. Forecasting the energy consumption of China by the grey prediction model[J]. Energy Sources Part B,2012,7 (4): 376-389.
[149]X.J.Wang, S.L.Yang, J.Ding. Dynamic GM (1,1) model based on cubic spline for electricity consumption prediction in smart grid[J]. China Communications,2010,7(4):83-88.
[150]Z.X.Wang,Y.G.Dang,S.F.Liu.The Optimization of Background Value in GM(1,1)Model[J].The Journal of Grey System,2007,10(2):69-74.
[151]Z.X.Wang, Y.G.Dang, S.W.He. The optimized GPM(1,1) for forecasting small sample oscillating series[J]. Grey System Theory Application,2012, 2(2):197-206.
[152]C.I.Chen, S.J.Huang. The necessary and sufficient condition for GM(1,1) grey prediction model[J]. Applied Mathematics and Computation,2013,219: 6152-6162.
[153]J.Z.Wang, X.L.Ma, J.Wu, YDong. Optimization models based on GM (1, 1) and seasonal fluctuation for electricity demand forecasting[J]. Electrical Power and Energy Systems,2012,43:109-117.
[154]Y.L.Huang, C.T.Lin. Developing an interval forecasting method to predict undulated demand[J]. Qual Quant,2011,45:513-524.
[155]U.Kumar, V.K. Jain. Time series models (Grey-Markov, Grey Model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India[J]. Energy,2010,35:1709-1716.
[156]S.L.Ou. Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm[J]. Computers and Electronics in Agriculture,2012,85:33-39.
[157]L.C.Hsu,Y.H.Wen.Application of Grey theory and multiobjective programming towards airline network design[J]. European Journal of Operational Research,2000,127:44-68.
[158]L.C.Hsu. Using improved grey forecasting models to forecast the output of opto-electronics industry[J]. Expert Systems with Applications, 2011,38:13879-13885.
[159]T.L.Tien. A research on the prediction of machining accuracy by the deterministic grey dynamic model DGDM(1,1,1)[J]. Applied Mathematics and Computation,2005,161:923-945.
[160]T.L.Tien. A research on the grey prediction model GM(l,n)[J]. Applied Mathematics and Computation,2012,218:4903-4916.
[161]P.Zhou, B.W.Ang, K.L.Poh. A trigonometric grey prediction approach to forecasting electricity demand[J]. Energy,2006,31:2839-2847.
[162]李翠凤,戴文战.基于函数cotx变换的灰色建模方法[J].系统工程,2005,23(3)：110-114.
[163]关叶青,刘思峰.基于函数cot(xα)变换的灰色GM(1,1)建模方法[J].系统工程,2008,26(9)：89-93.
[164]戴文战,熊伟,杨爱萍.基于函数cot(xα)变换及背景值优化的灰色建模[J].浙江大学学报(工学版),2010,44(7)：1368-1372.
[165]崔立志,刘思峰.基于数据变换技术的灰色预测模型[J].系统工程,2010,28(5)：104-107.
[166]陈超英.累加生成的改进和GM(1,1,t)灰色模型[J].数学的实践与认识,2007,37(2)：105-109.
[167]黄继,种晓丽.广义累加灰色预测控制模型及其优化算法[J].系统工程理论与实践,2009,29(6)：147-156.
[168]杨知,任鹏,党耀国.反向累加生成与GOM(1,1)模型的优化[J].系统工程理论与实践,2009,29(8)：160-164.
[169]熊萍萍,门可佩,吴香华.以x(1)(n)为初始条件的无偏GM(1,1)模型[J].南京信息工程大学学报,2009,1(3)：258-263.
[170]江南,刘小洋.基于Gauss公式的GM(1,1)模型的背景值构造新方法与应用[J].数学的实践与认识,2008,38(7)：90-94.
[171]R.T.Marler and J.S.Arora. Survey of multi-objective optimization methods for engineering[J]. Structural Multidisciplinary optimization, 2004,26: 369-395.
[172]A.Chinchuluun.P.M.Pardalos. A survey of recent developments in multi-objective Optimization[J]. Annals Operation Research,2007,154: 29-50.
[173]M.Jimenez, A.Bilbao. Pareto-optimal solutions in fuzzy multi-objective linear programming[J]. Fuzzy Sets and Systems,2009,160:2714-2721.
[174]M. Alamaniotis,A.Ikonomopoulos,L.H.Tsoukalas. Evolutionary Multi-objective Optimization of Kernel-Based Very-Short-Term Load Forecasting[J]. IEEE Transactions on Power Systems,2012,27(3): 1477-1484.
[175]S.Fan and R.J.Hyndman. Short-term load forecasting based on a semi-parametric additive model[J]. IEEE Transactions on Power Systems, 2012,27(1):134-141.
[176]J.Taylor. Short-term load forecasting with exponentially weighted methods[J]. IEEE Transactions on Power Systems,2012,27(1):458-464.
[177]A. Khosravi, S. Nahavandi, D. Creighton, and D. Srinivasan. Interval type-2 fuzzy logic systems for load forecasting:a comparative study[J]. IEEE Transactions on Power Systems,2012,27(3):1274-1282.
[178]M.Ozlen, M.Azizo glu, B.A.Burton. Optimising a nonlinear utility function in multi-objective integer programming[J]. Journal Global Optimization,2013,56:93-102.
[179]J.M.Jorge. An algorithm for optimizing a linear function over an integer efficient set[J] European Journal Operational Research,2009,195(1):98-103.
[180]C.Dhaenens, J.Lemesre, E.G.Talbi. K-PPM:a new exact method to solve multi-objective combinatorial optimization problems[J]. European Journal Operational Research,2010,200(1):45-53.
[181]Z.W.Shang, L.F.Zhang, S.J.Ma, B.Fang and T.P.Zhang. Incomplete time series prediction using max-margin classification of data with absent features [J]. Mathematical Problems in Engineering,2010, Article ID:513810,14 pages.
[182]R.Weron. Modeling and forecasting electricity loads and prices:a statistical approach[M]. England:John Wiley & Sons Ltd,2006.
[183]Z.X.Guo, W.K.Wongb, Z.Li, P.Y.Ren. Modeling and Pareto optimization of multi-objective order scheduling problems in production planning[J]. Computers and Industrial Engineering,2013,64:972-986.
[2]牛东晓,曹树华,赵磊,等.电力负荷预测技术及其应用[M].北京：中国电力出版社,1998.
[3]赵希正.中国电力负荷特性分析与预测[M].北京：中国电力出版社,2002.
[4]鞠平.电力系统建模理论与方法[M].北京：科学出版社,2010.
[5]H.K.Alfares, M.Nazeeruddin. Electric load forecasting:literature survey and classification of methods[J]. International Journal of Systems Science, 2002,33:23-34.
[6]H.Hahn, S.M.Nieberg, S.Pickl. Electric load forecasting methods:tools for decision making[J]. European Journal of Operational Research, 2009,199(3):902-907.
[7]E.Almeshaiei, H.Saltan. A methodology for electric power load forecasting[J]. Alexandria Engineering Journal 2011,5:137-144.
[8]L.A.Zadeh. Fuzzy sets[J]. Information and Control,1965:338-353.
[9]L.A.Zadeh. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy Sets and Systems,1978:3-28.
[10]H.Tanaka, S.Uegima, K.Asai. Linear regression analysis with fuzzy model[J]. IEEE Transactions Systems Man Cybernet,1982,12:903-907.
[11]H.Tanaka. Fuzzy data analysis by possibilistic linear models[J]. Fuzzy Sets and Systems,1987,24:363-375.
[12]H.J.Zimmermann. Fuzzy Sets Theory and its Applications[M]. Kluwer, Boston, MA,1985.
[13]M.Hojati, C.R.Bector, K.Smimou. A simple method for computation of fuzzy linear regression [J]. European Journal of Operational Research, 2005,166:172-184.
[14]P. Diamond. Fuzzy least squares[J]. Information Sciences, 1998,46:141-157.
[15]C.L.Hor, S.J.Watson, S.Majithia. Analyzing the impact of weather variables on monthly electricity demands[J]. IEEE Transactions on Power Systems,2005,20 (4):2078-2085.
[16]M.Kelkinnama,S.M.Taheri. Fuzzy least-absolutes regression using shape preserving operations[J]. Information Sciences,2012,214:105-120.
[17]H.Shakouri, R.Nadimi. Outlier detection in fuzzy linear regression with crisp input-output by linguistic variable view[J]. Applied Soft Computing, 2013,13:734-742.
[18]T.Y.Chou, G.S.Liang, T.C.Han. Application of fuzzy regression on air cargo volume forecast[J]. Qual Quant,2013,47:897-908.
[19]G.E.P.Box, G.M.Jenkins. Time Series Analysis[M]. Forecasting and Control, Holden-Day, San Francisco,1970.
[20]D.Pfeffermann, J.Allon. Multivariate exponential smoothing:Methods and practice[J]. International Journal of Forecasting,1989,5:83-98.
[21]P.J.Brockwell,R.A.Davis.Time Series:Theory and Methods[M].2nd Springer-Verlag,1991.
[22]J.W.Taylor. Exponential smoothing with a damped multiplicative trend[J]. International Journal of Forecasting,2003,19:273-289.
[23]J.G.DeGooijer, R.J.Hyndman.25 years of time series forecasting[J]. International Journal of Forecasting,2006,22:443-473.
[24]Y.S.Lee, L.I.Tong. Forecasting nonlinear time series of energy consumption using a hybrid dynamic model[J]. Applied Energy,2012,94:251-256.
[25]M.Stepnicka, P.Cortez, J.P.Donate, L.Stepnickova. Forecasting seasonal time series with computational intelligence:On recent methods and the potential of their combinations[J]. Expert Systems with Applications,2013, 40:1981-1992.
[26]M.Bozic, M.Stojanovic, Z.Stajic, et al. Mutual Information-Based Inputs Selection for Electric Load Time Series Forecast ing [J]. Entropy,2013,15: 926-942.
[27]J.L.Deng. The Control problem of grey systems [J]. Systems&Control Letter,1982,1(5):288-294.
[28]S.F.Liu, YXin. Grey information[M]. New York:Springer,2006.
[29]L.F.Wu, S.F. Liu L.G..Yao,etal.Grey system model with the fractional order accumulation Commun Nonlinear Sci Numer Simulat,2013,18:1775-1785.
[30]L.F.Wu, S.F. Liu L.G..Yao,etal. The effect of sample size on the Grey system model[J]. Applied Mathematical Modelling,2013,37:6577-6583.
[31]C.C.Hsu, C.Y.Chen. Applications of improved Grey prediction model for power demand forecasting[J]. Energy Conversion and Management, 2003,44:2241-2249.
[32]焦润海,苏辰隽,林碧英等.基于气象信息因素修正的灰色短期负荷预测模型[J].电网技术,2013,37(3)：720-725.
[33]D.C.Park, M.A.El-SharKawi, R.J.Marks, etal. Electric load forecasting using a neural network[J].IEEE Transactions on Power Systems,1991,6(2): 442-449.
[34]H.S.Hippert, C.E.Pedreira, R.C.Souza. Neural networks for short-term load forecasting:A review and evaluation[J]. IEEE Transactions on Power Systems,2001,16(1):44-55.
[35]H.S.Hippert, D.W.Bunn, R.C.Souza. Large neural networks for electricity load forecasting:Are they overfitted[J]. International Journal of Forecasting, 2005,21:425-434.
[36]L.Hernandez, C.Baladr6n, J.M.Aguiar, et al. Short-Term Load Forecasting for Microgrids Based on Artificial Neural Networks[J]. Energies,2013,6: 1385-1408.
[37]U.Yolcu, E.Egrioglu, C.H.Aladag. A new linear & nonlinear artificial neural network model for time series forecasting[J]. Decision Support Systems, 2013,54:1340-1347.
[38]D.Singhal, K.S.Swarup. Electricity price forecasting using artificial neural networks[J]. Electrical Power and Energy Systems,2011,33:550-555.
[39]C.Hamzacebi. Improving artificial neural networks performance in seasonal time series forecasting[J]. Information Sciences,2008,178:4550-4559.
[40]S.C.Pandian, K.Duraiswamy, C.C.A.Rajan, N.Kanagaraj. Fuzzy approach for short term load forecasting[J]. Electric Power Systems Research, 2006,76:541-548.
[41]P.F.Pai. Hybrid ellipsoidal fuzzy systems in forecasting regional electricity loads[J]. Energy Conversion and Management,2006,47:2283-2289.
[42]L.C.Ying, M.C.Pan. Using adaptive network based fuzzy inference system to forecast regional electricity loads[J]. Energy Conversion and Management,2008,49:205-211.
[43]V.Vapnik. The Nature of Statistical Learning[M]. New York, Springer,1995.
[44]B.J.Chen, M.W.Chang, C.J.Lin. Load forecasting using support vector machines:A study on EUNITE competition[J]. IEEE Transactions on Power Systems,2001,19 (4):1821-1830.
[45]J.Wang, Y.Zhou, Y.Chen. Electricity load forecasting based on support vector machines and simulated annealing particle swarm optimization algorithm[C]. Proceedings of the IEEE International Conference on Automation and Logistics,2007:2836-2840.
[46]P.F.Pai, W.C.Hong. Forecasting regional electricity load based on recurrent support vector machines with genetic algorithms [J]. Electric Power Systems Research,2005,74(3):417-425.
[47]D.X.Niu, Y.L.Wang,D.D.Wu. Power load forecasting using support vector machine and ant colony optimization[J]. Expert Systems with Applications,2010,37(3):2531-2539.
[48]A. Miranian,M.Abdollahzade. Developing a Local Least-Squares Support Vector Machines-Based Neuro-Fuzzy Model for Nonlinear and Chaotic Time Series Prediction[J]. IEEE Transactions on Neural Networks and Learning Systems,2013,24(2):207-218.
[49]A. Mellit, A. Massi Pavan, M. Benghanem. Least squares support vector machine for short-term prediction of meteorological time series[J]. Theor Appl Climatol,2013,111:297-307.
[50]M.Alamaniotis, A.Ikonomopoulos, L.H.Tsoukalas. Evolutionary Multiobjective Optimization of Kernel-Based Very-Short-Term Load Forecasting[J]. IEEE Transactions on Power Systems,2012,27(3): 1477-1484.
[51]N. Amjady, A. Daraeepour. Midterm demand prediction of electrical power systems using a new hybrid forecasting technique[J].IEEE Transactions on Power Systems,2011,26(2):755-765.
[52]R.A.Hooshmand, H.Amooshahi, M.Parastegari. A hybrid intelligent algorithm based short-term load forecasting approach[J]. International Journal of Electrical Power & Energy Systems,2013,45(1):313-324.
[53]Q.Song, B.S.Chissom. Fuzzy time series and its models[J]. Fuzzy Sets System,1993,54:269-277.
[54]Q.Song, B.S.Chissom. Forecasting enrollments with fuzzy time series-Part 1[J]. Fuzzy Sets System,1993,54:1-9.
[55]Q.Song, B.S.Chissom. Forecasting enrollments with fuzzy time series-Part 2[J]. Fuzzy Sets System,1994,62:1-8.
[56]S.M.Chen. Forecasting enrollments based on fuzzy time series[J]. Fuzzy Sets System,1996,81:311-319.
[57]S.M.Chen. Forecasting enrollments based on high-order fuzzy time series[J]. Cybernetics and Systems:An International Journal,2002,33:1-16.
[58]S.M.Chen, J.R.Hwang. Temperature prediction using fuzzy time series[J]. IEEE Transactions System Man Cybernation. Part B,2000,30(2):263-275.
[59]S.M.Chen, N.Y.Chung. Forecasting enrollments using high-order fuzzy time series and genetic algorithms [J]. International Journal of Intelligent Systems,2006,21(5):485-501.
[60]S.M.Chen and N.Y.Chung. Forecasting enrollments of students by using fuzzy time series and genetic algorithms [J]. Information and Management Sciences,2006,17(3):1-17.
[61]K.H.Huarng. Effective lengths of intervals to improve forecasting in fuzzy time series[J]. Fuzzy Sets System,2001,123:387-394.
[62]K.H.Huarng,T.H.K.Yu. Ratio-based lengths of intervals to improve fuzzy time series forecasting[J]. IEEE Transactions System Man Cybernation, Part B,2006,36(2):328-340.
[63]K.H.Huarng, T.H.K.Yu. A multivariate heuristic model for fuzzy time-series forecasting[J]. IEEE Transaction System Man Cybernation, Part B,2007, 37(4):836-846.
[64]C.H.Cheng, R.J.Chang, C.A.Yeh. Entropy-based and trapezoidal fuzzification-based fuzzy time series approach for forecasting IT project cost[J]. Technological Forecasting and Social Change,2006,73(5): 524-542.
[65]C.H.Cheng, T.L.Chen, H.J.Teoh, C.H.Chiang. Fuzzy time-series based on adaptive expectation model for TAIEX forecasting[J]. Expert Systems with Applications,2008,34:1126-1132.
[66]C.H.Cheng, G.W.Cheng.J.W.Wang. Multi-attribute fuzzy time series method based on fuzzy clustering[J]. Expert Systems with Applications, 2008,34,1235-1242.
[67]S.T.Li, Y.C.Cheng, and S.Y.Lin. A FCM-based deterministic forecasting model for fuzzy time series[J]. Computers and Mathematics with Applications,2008,56(12):3052-3063.
[68]I.H.Kuo, S.J.Horng, T.W.Kao,et al. An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization [J]. Expert Systems with Applications,2009,36(3):6108-6117.
[69]R.C.Tsaur, J.C.O.Yang, and H.F.Wang. Fuzzy relation analysis in fuzzy time series model [J]. Computers and Mathematics with Applications,2005,49:539-548.
[70]L.W.Lee, L.H.Wang, S.M.Chen, et.al. Handling forecasting problems based on two-factors high-order fuzzy time series[J]. IEEE Transactions Fuzzy System,2006,14(3):468-477.
[71]C.H.Aladag, M.A.Basaran, E.Egrioglu, U.Yolcu, and V.R.Uslu. Forecasting in high order fuzzy time series by using neural networks to define fuzzy relations[J]. Expert Systems with Applications,2009,36(3):4228-4231.
[72]Y.Y.Hsu, S.M.Tse, B.Wu. A new approach of bivariate fuzzy time series analysis to the forecasting of a stock index[J]. Internal Journal Uncertainty Fuzziness Knowledge-Based System,2003,11(6):671-690.
[73]U.Yolcu, E.Egrioglu, V.R.Uslu, M.A.Basaran,C.H.Aladag. A new approach for determining the length of intervals for fuzzy time series[J]. Applied Soft Computing,2009,9:647-651.
[74]E.Egrioglu, C.H. Aladag, U.Yolcu, M.A.Basaran &, V.R.Uslu. A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model[J]. Expert Systems with Applications, 2009,36:7424-7434.
[75]E.Egrioglu, C.H. Aladag, U.Yolcu, V.R.Uslu & M.A.Basaran. A new approach based on artificial neural networks for high order multivariate fuzzy time series[J]. Expert Systems with Applications,2009,36: 10589-10594.
[76]E.Egrioglu, C.H. Aladag, U.Yolcu, V.R.Uslu & M.A.Basaran. Finding an optimal interval length in high order fuzzy time series [J]. Expert Systems with Applications,2010,37:5052-5055.
[77]E.Egrioglu, C.H. Aladag, M.A.Basaran, V.R.Uslu, V.R.Uslu. A new approach based on the optimization of the length of intervals in fuzzy time series[J]. Journal of Intelligent and Fuzzy Systems,2011,22:15-19,
[78]E.Egrioglu, C.H. Aladag, U.Yolcu, V.R.Uslu & N.A.Erilli.Fuzzy time series forecasting method based on Gustafson-Kessel fuzzy clustering[J]. Expert Systems with Applications,2011,38:10355-10357.
[79]E.Egrioglu, C.H.Aladag, U.Yolcu. Fuzzy time series forecasting with a novel hybrid approach combining fuzzy c-means and neural networks[J]. Expert Systems with Applications,2013,40:854-857.
[80]F.M.Tseng, G.H.Tzeng, H.C.Yu,et al. Fuzzy ARIMA model for forecasting the foreign exchange market[J]. Fuzzy Sets System,2001,18:9-19.
[81]J.R.Poulsen. Fuzzy Time Series Forecasting[D]. Aalborg University Esbjerg (AAUE),2009.
[82]H.Saima, JJafreezal, B.S.Brahim, A.J.Tahseen. A Hybrid Fuzzy Time Series Model for Forecasting[J]. Engineering Letters,2012:1-6.
[83]R. Mamlook, O. Badran and E. Abclulhadi. A fuzzy inference model for short term load forecasting [J]. Energy Policy,2009,37(4):1239-1248.
[84]H.T.Liu, N.C.Wei, C.G.Yang. Improved time-variant fuzzy time series Forecast[J]. Fuzzy Optimization Decision Making,2009,8(1):45-65.
[85]C.A.Maia, M.M.Goncalves. Application of switched adaptive system to load forecasting [J] Electric power systems research,2008,78(5):721-727.
[86]H.K.Yu. Weighted fuzzy time series models for TAIEX forecasting [J]. Physica A,2005,349:609-624.
[87]C.H.Cheng,T.L.Chen,C.H.Chian.Trend-weighted fuzzy time seride model for TAIEX Forecasting[C].Lecture Notes in Computer Science,2006, 4234:469-477.
[88]H.J.Teoh,T.L.Chen,C.H.Cheng. Frequency-weighted fuzzy time-series based on Fibonacci sequence for TAIEX forecasting[C]. Lecture Notes in Computer Science,2007,4819:27-34.
[89]W.K.Wong, E.J.Bai, W.C.Chu. Adaptive time-variant models for fuzzy time-series forecasting[J]. IEEE Transactions on Systems Man and Cybernetics-Part B:Cybernetics 2010,40(6):1531-1534.
[90]X.J.Liu, E.J.Bai, J.A.Fang and L.H.Luo. Time-Variant Slide Fuzzy Time-series Method for Short-Term Load Forecasting [C].2010 IEEE ICIS (Intelligent Computing and Intelligent Systems) 2010,1:65-68.
[91]刘晓娟,方建安.综合权重的模糊时间序列的电力负荷预测方法[J].华东电力,2012,40(4)：518-520.
[92]X.J.Liu, E.J.Bai, J.A.Fang. Weighted Time-variant Slide Fuzzy Time-series Models for Short-Term Load Forecasting[J]. Journal of Intelligent Learning Systems and Applications,2012,4:285-290.
[93]E.J.Bai, W.C.Chu, W.K.Wong, Xia M, Pan F. A heuristic time-invariant model for fuzzy time series forecasting [J]. Expert Systems with Applications,2011,38(3):2701-2707.
[94]姜学宝,吴强.苏州电网负荷和敏感性分析[J].江苏电机工程,2009,28(6)：45-48.
[95]D.T. Redden, W.H.Woodall. Properties of certain fuzzy linear regression methods[J]. Fuzzy Sets and Systems,1994,64(3):361-375.
[96]P.F.Christoffersen. Evaluating interval forecasts[J]. International Economic Review,1998,39(4):841-862.
[97]B.Kim, R.R.Bishu. Evaluation of fuzzy linear regression models by comparison membership function[J]. Fuzzy Sets and Systems,1998,100(1): 343-352.
[98]R.C.Tsaur, H.F.Wang, J.C.O.Yang. Fuzzy regression for seasonal time series analysis[J]. International Journal of Information Technology and Decision Making,2002,1(1):165-175.
[99]R.C.Tsaur. Forecasting analysis by using fuzzy grey regression model for solving limited time series data[J]. Soft Computing,2008,12:1105-1113.
[100]R.C.Tsaur. The development of an interval grey regression model for limited time series forecasting [J]. Expert Systems with Applications, 2010,37:1200-1206.
[101]J.R.Yu, G.H.Tzeng, H.L.Li. A general piecewise necessity regression analysis based on linear programming[J]. Fuzzy Sets and Systems, 1999,105(3):429-436.
[102]D.H.Hong, S.H.Lee, H.Y..Do, Fuzzy linear regression analysis for fuzzy input-output data using shape-preserving operations[J]. Fuzzy Set and Systems,2001,122:513-526.
[103]D.H.Hong, J.K.Song, H.Y.Do. Fuzzy least squares linear regression analysis using shape preserving operation [J].Information Sciences,2001, 138(1):185-193.
[104]M.S.Yang, T.S.Lin. Fuzzy least-squares linear regression analysis for fuzzy input-output data[J]. Fuzzy Sets and Systems,2002,126(3):389-399.
[105]M.S.Yang, H.H.Liu. Fuzzy least-squares algorithms for interactive fuzzy linear regression models[J]. Fuzzy Sets and Systems,2003,135(2): 305-316.
[106]K.B.Song, Y.S.Baek, D.H.Hong, etc. Short-Term Load Forecasting for the holidays using fuzzy linear regression method. Transactions on power systems 2005,20(1):96-101.
[107]S.H.Choi, J.J.Buckley. Fuzzy regression using least absolute deviation estimators[J].Soft Computing,2008,12:257-263.
[108]M.M.Nasrabadi, E.Nasrabadi. A mathematical programming approach to fuzzy linear regression analysis[J]. Applied Mathematics and Computation, 2004,155(3):873-881.
[109]M.M.Nasrabadi, E.Nasrabadi,A.R.Nasrabady. Fuzzy linear regression analysis:a multi-objective programming approach[J].Applied Mathematics and Computation,2005,163:245-251.
[110]黄华,宋艳萍,苗新艳等.基于多目标规划法的模糊线性回归分析[J].模糊系统与数学,2012,26(3)：114-119.
[111]M.Hojati, C.R.Bector, K.Smimou. A simple method for computation of fuzzy linear regression [J]. European Journal of Operational Research,2005,166:172-184.
[112]Q.Wu. Fuzzy fault diagnosis based on fuzzy robust v-support vector classifier and modified genetic algorithm [J]. Expert Systems with Applications,2011,38:4882-4888.
[113]Q.Wu. The complex fuzzy system forecasting model based on triangular fuzzy robust wavelet m-support vector machine[J]. Expert Systems with Applications,2011,38:14478-14489.
[114]A.Bolotin. Robustness of the regression models for uncertain categories [J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2007,15(6):681-695.
[115]H.C.Wu. Linear regression analysis for fuzzy input and output data using the extension principle [J].Computers Mathematics with Application,2003, 45(12):1849-1859.
[116]P.Durso,T.Gastaldi. A least-squares approach to fuzzy linear regression analysis[J]. Computation Statistics and Data Analysis,2000,34(4): 427-440.
[117]A.Bargiela,W.Pedrycz, T.Nakashima. Multiple regression with fuzzy data[J]. Fuzzy Sets and Systems,2007,158:2169-2188.
[118]A.Bisserier,R.Boukezzoula,S.Galichet. Linear fuzzy regression using trapezoidal fuzzy intervals [J]. Journal of Uncertain Systems,2010,4(1): 59-72.
[119]A.Bisserier, R.Boukezzoula, S.Galichet. A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals[J]. Information Sciences, 2010,180(19):3653-3673.
[120]E.Nasrabadi,S.M.Hashemi. Robust fuzzy regression analysis using neural networks[J]. International Journal Uncertainty, Fuzziness and Knowledge-Based Systems,2008,16:579-598.
[121]Y.L.Huang, C.T.Lin. Developing an interval forecasting method to predict undulated demand[J]. Qual Quant,2011,45(3):513-524.
[122]Y.M.Wi, S.K.Joo and K.B.Song. Holiday load forecasting using fuzzy polynomial regression with weather feature selection and adjustment[J]. IEEE Transactions on Power Systems,2012,27(2):596-603.
[123]H.Katagiri, T.Uno, K.Kato, etal. Random fuzzy multi-objective linear programming:Optimization of possibilistic value at risk (pVaR)[J].Expert Systems with Applications,2013,40:563-574.
[124]P.J.Rousseeuw, A.M.Leroy. Robust Regression&Outliers Detection[M]. John Wiley and Sons Inc., Hoboken, NJ,2001.
[125]P.D'Urso, R.Massari, A.Santoro. Robust fuzzy regression analysis[J]. Information Sciences,2011,181:4154-4174.
[126]T.D.Nguyen, R.Welsch. Outlier detection and least trimmed squares approximation using semi-definite programming[J]. Computational Statistics and Data Analysis,2010,54(12):3212-3226.
[127]K.Shibata, J.Watada, Y.Yabuuchi. A fuzzy regression approach for evaluating electric and electronics corporations[J]. Journal of Japan Industrial Management Associations,2008,59(1):58-67.
[128]S.Varga. Robust estimations in classical regression models versus robust estimations in fuzzy regression models[J]. Kybernetika,2007,43 (4):503-508.
[129]T.Torabi, J.Behboodian. Fuzzy least-absolutes estimates in linear models[J]. Communications in Statistics:Theory and Methods,2007,36 (10):1935-1944.
[130]B.Y. Sohn. Robust fuzzy linear regression based on M-estimators [J]. Journal of Application Mathematics and Computing,2005,18(1):591-601.
[131]M.C.Ortiz, L.A.Sarabia, A.Herrero. Robust regression techniques A useful alternative for the detection of outlier data in chemical analysis[J]. Talanta, 2006,70:499-512.
[132]Y.Chakhchoukh. A new robust estimation method for short-term load forecasting [C].17th European Signal Processing Conference, EUSIPCO 2009:2489-2493.
[133]Y.Chakhchoukh, P.Panciatici, L.Mili. Electric load forecasting based on statistical robust methods[J]. IEEE Transactions on Power Systems,2007, 6(1):1-12.
[134]Y.Chakhchoukh. A new robust estimation method for ARMA models[J]. IEEE Transactions on signal processing,2010,58(7):3512-3522.
[135]Z.M.Song, X.P.Xiao,J.L.Deng.The character of opposite direction AGO and class ratio[J].The Journal of Grey System,2002,14(1):9-14.
[136]D.Akay, M.Atak.Grey prediction with rolling mechanism for electricity demand forecasting of Turkey[J]. Energy,2007,32:1670-1675.
[137]Y.H.Lin, P.C.Lee. Novel high precision grey forecasting model[J], Automation in Construction,2007,16:771-777.
[138]Y.H.Lin, P.C.Lee, T.P.Chang. Adaptive and high-precision grey forecasting model[J]. Expert System and Applications,2009,36:9658-9662.
[139]Z.Zhao, J.Z.Wang,J.Zhao,et al. Using a grey model optimized by differential evolution algorithm to forecasting the per capita annual net income of rural households in china[J]. Omega,2012,40:525-532.
[140JN.M. Xie, S.F. Liu. Discrete grey forecasting model and its optimization[J]. Applied Mathematical Modeling,2009,33:1173-1186.
[141]N.M.Xie, S.F.Liu,Y.J.Yang,C.Q.Yuan. On novel grey forecasting model based on non-homogeneous index sequence[J]. Applied Mathematical Modeling,2013,37:5059-5068.
[142]T.X.Yao, S.F.Liu and N.M.Xie. On the properties of small sample of GM(1,1) model[J]. Applied Mathematical Modeling,2009,33:1894-1903.
[143]B.zeng, S.F.Liu and N.M.Xie. Prediction model of interval grey number based on DGM(1,1)[J]. Journal of Systems Engineering and Electronics, 2010,21(4):598-603.
[144]J.Cui, S.F.Liu, B.Zeng, N.M.Xie. A novel grey forecasting model and its optimization[J]. Applied Mathematical Modeling,2013,37:4399-4406.
[145]L.F.Wu, S.F.Liu,Y.N.Wang. Grey Lotka-Volterra model and its application[J]. Technological Forecasting & Social Change,2012,79: 1720-1730.
[146]L.F.Wu, S.F.Liu, L.G.Yao,S.L.Yan, D.L.Liu. Grey system model with the fractional order accumulation [J]. Communications in Nonlinear Science and Number Simulation,2013,18:1775-1785.
[147]E.Kayacan, B.Ulutas, O-Kaynak. Grey system theory-based models in time series prediction[J]. Expert Systems with Applications,2010,37: 1784-1789.
[148]S. J.Feng, YD.Ma, Z.L.Song. Forecasting the energy consumption of China by the grey prediction model[J]. Energy Sources Part B,2012,7 (4): 376-389.
[149]X.J.Wang, S.L.Yang, J.Ding. Dynamic GM (1,1) model based on cubic spline for electricity consumption prediction in smart grid[J]. China Communications,2010,7(4):83-88.
[150]Z.X.Wang,Y.G.Dang,S.F.Liu.The Optimization of Background Value in GM(1,1)Model[J].The Journal of Grey System,2007,10(2):69-74.
[151]Z.X.Wang, Y.G.Dang, S.W.He. The optimized GPM(1,1) for forecasting small sample oscillating series[J]. Grey System Theory Application,2012, 2(2):197-206.
[152]C.I.Chen, S.J.Huang. The necessary and sufficient condition for GM(1,1) grey prediction model[J]. Applied Mathematics and Computation,2013,219: 6152-6162.
[153]J.Z.Wang, X.L.Ma, J.Wu, YDong. Optimization models based on GM (1, 1) and seasonal fluctuation for electricity demand forecasting[J]. Electrical Power and Energy Systems,2012,43:109-117.
[154]Y.L.Huang, C.T.Lin. Developing an interval forecasting method to predict undulated demand[J]. Qual Quant,2011,45:513-524.
[155]U.Kumar, V.K. Jain. Time series models (Grey-Markov, Grey Model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India[J]. Energy,2010,35:1709-1716.
[156]S.L.Ou. Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm[J]. Computers and Electronics in Agriculture,2012,85:33-39.
[157]L.C.Hsu,Y.H.Wen.Application of Grey theory and multiobjective programming towards airline network design[J]. European Journal of Operational Research,2000,127:44-68.
[158]L.C.Hsu. Using improved grey forecasting models to forecast the output of opto-electronics industry[J]. Expert Systems with Applications, 2011,38:13879-13885.
[159]T.L.Tien. A research on the prediction of machining accuracy by the deterministic grey dynamic model DGDM(1,1,1)[J]. Applied Mathematics and Computation,2005,161:923-945.
[160]T.L.Tien. A research on the grey prediction model GM(l,n)[J]. Applied Mathematics and Computation,2012,218:4903-4916.
[161]P.Zhou, B.W.Ang, K.L.Poh. A trigonometric grey prediction approach to forecasting electricity demand[J]. Energy,2006,31:2839-2847.
[162]李翠凤,戴文战.基于函数cotx变换的灰色建模方法[J].系统工程,2005,23(3)：110-114.
[163]关叶青,刘思峰.基于函数cot(xα)变换的灰色GM(1,1)建模方法[J].系统工程,2008,26(9)：89-93.
[164]戴文战,熊伟,杨爱萍.基于函数cot(xα)变换及背景值优化的灰色建模[J].浙江大学学报(工学版),2010,44(7)：1368-1372.
[165]崔立志,刘思峰.基于数据变换技术的灰色预测模型[J].系统工程,2010,28(5)：104-107.
[166]陈超英.累加生成的改进和GM(1,1,t)灰色模型[J].数学的实践与认识,2007,37(2)：105-109.
[167]黄继,种晓丽.广义累加灰色预测控制模型及其优化算法[J].系统工程理论与实践,2009,29(6)：147-156.
[168]杨知,任鹏,党耀国.反向累加生成与GOM(1,1)模型的优化[J].系统工程理论与实践,2009,29(8)：160-164.
[169]熊萍萍,门可佩,吴香华.以x(1)(n)为初始条件的无偏GM(1,1)模型[J].南京信息工程大学学报,2009,1(3)：258-263.
[170]江南,刘小洋.基于Gauss公式的GM(1,1)模型的背景值构造新方法与应用[J].数学的实践与认识,2008,38(7)：90-94.
[171]R.T.Marler and J.S.Arora. Survey of multi-objective optimization methods for engineering[J]. Structural Multidisciplinary optimization, 2004,26: 369-395.
[172]A.Chinchuluun.P.M.Pardalos. A survey of recent developments in multi-objective Optimization[J]. Annals Operation Research,2007,154: 29-50.
[173]M.Jimenez, A.Bilbao. Pareto-optimal solutions in fuzzy multi-objective linear programming[J]. Fuzzy Sets and Systems,2009,160:2714-2721.
[174]M. Alamaniotis,A.Ikonomopoulos,L.H.Tsoukalas. Evolutionary Multi-objective Optimization of Kernel-Based Very-Short-Term Load Forecasting[J]. IEEE Transactions on Power Systems,2012,27(3): 1477-1484.
[175]S.Fan and R.J.Hyndman. Short-term load forecasting based on a semi-parametric additive model[J]. IEEE Transactions on Power Systems, 2012,27(1):134-141.
[176]J.Taylor. Short-term load forecasting with exponentially weighted methods[J]. IEEE Transactions on Power Systems,2012,27(1):458-464.
[177]A. Khosravi, S. Nahavandi, D. Creighton, and D. Srinivasan. Interval type-2 fuzzy logic systems for load forecasting:a comparative study[J]. IEEE Transactions on Power Systems,2012,27(3):1274-1282.
[178]M.Ozlen, M.Azizo glu, B.A.Burton. Optimising a nonlinear utility function in multi-objective integer programming[J]. Journal Global Optimization,2013,56:93-102.
[179]J.M.Jorge. An algorithm for optimizing a linear function over an integer efficient set[J] European Journal Operational Research,2009,195(1):98-103.
[180]C.Dhaenens, J.Lemesre, E.G.Talbi. K-PPM:a new exact method to solve multi-objective combinatorial optimization problems[J]. European Journal Operational Research,2010,200(1):45-53.
[181]Z.W.Shang, L.F.Zhang, S.J.Ma, B.Fang and T.P.Zhang. Incomplete time series prediction using max-margin classification of data with absent features [J]. Mathematical Problems in Engineering,2010, Article ID:513810,14 pages.
[182]R.Weron. Modeling and forecasting electricity loads and prices:a statistical approach[M]. England:John Wiley & Sons Ltd,2006.
[183]Z.X.Guo, W.K.Wongb, Z.Li, P.Y.Ren. Modeling and Pareto optimization of multi-objective order scheduling problems in production planning[J]. Computers and Industrial Engineering,2013,64:972-986.