基于IOWC-GOWA算子及相对熵的区间型组合预测模型
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摘要
针对用区间型数据描述不确定现象的组合预测问题,为了提高区间型数据的预测精度,首先采用诱导有序加权连续区间的广义有序加权平均(IOWC-GOWA)算子将区间数集结为实数;然后对集结后的实数进行标准化处理;最后从信息论的角度引入相对熵作为最优准则,提出了基于IOWC-GOWA算子及相对熵的区间型组合预测模型;另外,通过实例分析了该组合预测模型的合理性和有效性;结果表明:该组合预测模型可以有效地提高区间型数据的预测精度,即该模型是合理有效的,并且,参数λ和BUM函数的选取会对模型的预测精度产生一定的影响。
Aiming at combination forecasting problems of describing uncertainty by interval numbers,in order to improve the forecasting accuracy of interval data,firstly,the induced ordered weighted continuous generalized ordered weighted averaging( IOWC-GOWA) operator is used to aggregate the interval numbers into real numbers,then we normalize them. Finally,by introducing relative entropy as the optimum criterion from the perspective of information theory,an interval combination forecasting model based on IOWC-GOWA operator and relative entropy is proposed. Furthermore,the rationality and effectiveness of the combined forecasting model is analyzed by an example. The results show that the combination forecasting model can effectively improve the forecasting accuracy of interval data. That is to say,the model is reasonable and effective. Additionally,the selection of the parameter λand the BUM function has a certain impact on the prediction accuracy of the model.
Aiming at combination forecasting problems of describing uncertainty by interval numbers,in order to improve the forecasting accuracy of interval data,firstly,the induced ordered weighted continuous generalized ordered weighted averaging( IOWC-GOWA) operator is used to aggregate the interval numbers into real numbers,then we normalize them. Finally,by introducing relative entropy as the optimum criterion from the perspective of information theory,an interval combination forecasting model based on IOWC-GOWA operator and relative entropy is proposed. Furthermore,the rationality and effectiveness of the combined forecasting model is analyzed by an example. The results show that the combination forecasting model can effectively improve the forecasting accuracy of interval data. That is to say,the model is reasonable and effective. Additionally,the selection of the parameter λand the BUM function has a certain impact on the prediction accuracy of the model.
引文
[1] BATES J M, GRANGER C W J. Combination of Forecasts[J]. Operations Research Quarterly,1969,20(4):451—468
[2] ELLIOTT G, GRANGER C W J, Timmermann A.Handbook of Economic Forecasting(Volume 1)[M].North-Holland:Elsevier,2006
[3] ARMSTRONG J. Principles of Forecasting[M]. Boston:Kluwer Academic,2001
[4] LAMBERSON P J, PAGE S E. Optimal Forecasting Groups[J]. Management Science, 2012, 58(4):805—810
[5]唐小我,马永开,曾勇等.现代组合预测和组合投资决策方法及应用研究[M].北京:科学出版社,2003TANG X W,MA Y K,ZENG Y,et al. Research on Modern Combined Forecasting and Combined Investment Decision-making Method and Its Application[M].Beijing:Science Press,2003(in Chinese)
[6]陈华友.组合预测方法有效性理论及其应用[M].北京:科学出版社,2008CHEN H Y. Effectiveness Theory of Combined Forecasting Method and Its Application[M]. Beijing:Science Press,2008(in Chinese)
[7]张晓芳,杨桂元,钟梅.基于IOWHA算子的对外直接投资组合预测[J].重庆工商大学学报(自然科学版),2016,33(3):76—81ZHANG X F,YANG G Y,ZHONG M. Outward Foreign Direct Investment Based on IOWHA Operator[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2016,33(3):76—81(in Chinese)
[8]江立辉,陈华友,丁芳清,等.基于IOWC-GOWA算子的区间组合预测模型[J].计算机工程与应用,2015,51(3):50—54JIANG L H,CHEN H Y,DING F Q,et al. Combination Forecasting Model Based on Induced Ordered Weighted Continuous Generalized Ordered Weighted Averaging Operator[J]. Computer Engineering and Applications,2015,51(3):50—54(in Chinese)
[9]曹晓俊,袁宏俊.连续区间广义有序加权调和平均算子及其在区间组合预测中应用[J].南京理工大学学报,2017,41(1):123—131CAO X J,YUAN H J. Continuous Generalized Ordered Weighted Harmonic Averaging Operator and Its Applications in Interval Combination Forecasting[J].Journal of Nanjing University of Science and Technology,2017,41(1):123—131(in Chinese)
[10]张超,袁宏俊.一类诱导广义有序加权对数的连续区间有序加权调和平均算子及其应用[J].延边大学学报(自然科学版),2017,43(4):302—307ZHANG C,YUAN H J. A Class of Induced Generalized Ordered Weighted Logarithmic Continuous Ordered Weighted Harmonic Averaging(IGOWLC-OWHA)Operators and Its Applications[J]. Journal of Yanbian University(Natural Science Edition),2017,43(4):302—307(in Chinese)
[11]袁宏俊,胡凌云.基于连续区间有序几何加权平均Power算子的区间型组合预测模型[J].数理统计与管理,2019(2):270—280YUAN H J, HU L Y. The Interval Combination Forecasting Model Based on COWG-WPA Operator[J].Journal of Applied Statistics and Management,2019(2):270—280(in Chinese)
[12]张进.不同精度准则下的区间型组合预测方法研究[D].合肥:安徽大学,2010ZHANG J. The Research of Interval Combination Forecasting Methods under Different Accuracy Criteria[D]. Hefei:Anhui University,2010(in Chinese)
[13]吴潜.基于中点及半径的区间数组合预测模型性质研究[J].统计与决策,2017,(4):36—40WU Q. The Nature of the Study of Interval Number Combination Forecast Model Based on Midpoints and Radius[J]. Statistics and Decision,2017(4):36—40(in Chinese)
[14]袁宏俊,钟梅,吴庆鹏.基于IGOWLA算子的区间组合预测模型[J].统计与决策,2016(14):22—25YUAN H J, ZHONG M, WU Q P. The Interval Combination Prediction Model Based on IGOWLA Operator[J]. Statistics and Decision,2016(14):22—25(in Chinese)
[15]袁宏俊,韦晨珺娃,钟梅.基于联系数贴近度的区间型组合预测模型及其有效性[J].统计与信息论坛,2017,32(6):31—37YUAN H J,WEI C J W,ZHONG M. Research on Interval Combination Forecasting Model and Its Effectiveness Based on Contact Number Degree[J].Statistics and Information Forum,2017,32(6):31—37(in Chinese)
[16]林义征,袁宏俊,宋马林.基于IOWHA算子与向量夹角余弦的联系数型区间组合预测[J].统计与决策,2016,449(5):84—86LIN Y Z, YUAN H J, SONG M L. The Interval Combination Prediction of Coefficient Type Based on IOWHA Operator and Vectorial Angle Cosine[J].Statistics and Decision, 2016, 449(5):84—86(in Chinese)
[17] YAGER R R. OWA Aggregation over a Continuous Interval Argument with Applications to Decision Making[J]. IEEE Transactions on Systems, Man, and Cybernetics,Part B,2004,34(5):1952—1963
[18] YAGER R R. Generalized OWA Aggregation Operators[J]. Fuzzy Optimization and Decision Making,2004,3(1):93—107
[19] ZHOU L G,CHEN H Y. Continuous Generalized OWA Operator and Its Application to Decision Making[J].Fuzzy Sets and Systems,2011,168(10):18—34
[20]陈华友,刘春林.基于IOWA算子组合预测方法[J].预测,2003,22(1):61—65CHENG H Y, LIU C L. A Kind of Combination Forecasting Method Based on Induced Ordered Weighted Averaging(IOWA)Operators[J]. Forecasting,2003,22(1):61—65(in Chinese)
[21]赵萌,邱菀华,刘北上.基于相对熵的多属性决策排列方法[J].控制与决策,2010,25(7):1098—1104ZHAO M, QIU W H, LIU B S. Relative Entropy Evaluation Method for Multiple Attribute Decision Making[J]. Control and Decision,2010,25(7):1098—1104(in Chinese)
[22]徐惠莉,吴柏林,江韶珊.区间时间序列预测准确度探讨[J].数量经济技术经济研究,2008,12(1):133—140XU H L, WU B L, JIANG Y S. On Forecasting Efficiency Evaluation for Interval Time Series[J]. The Journal of Quantitative and Technical Economics,2008,12(1):133—140(in Chinese)
[2] ELLIOTT G, GRANGER C W J, Timmermann A.Handbook of Economic Forecasting(Volume 1)[M].North-Holland:Elsevier,2006
[3] ARMSTRONG J. Principles of Forecasting[M]. Boston:Kluwer Academic,2001
[4] LAMBERSON P J, PAGE S E. Optimal Forecasting Groups[J]. Management Science, 2012, 58(4):805—810
[5]唐小我,马永开,曾勇等.现代组合预测和组合投资决策方法及应用研究[M].北京:科学出版社,2003TANG X W,MA Y K,ZENG Y,et al. Research on Modern Combined Forecasting and Combined Investment Decision-making Method and Its Application[M].Beijing:Science Press,2003(in Chinese)
[6]陈华友.组合预测方法有效性理论及其应用[M].北京:科学出版社,2008CHEN H Y. Effectiveness Theory of Combined Forecasting Method and Its Application[M]. Beijing:Science Press,2008(in Chinese)
[7]张晓芳,杨桂元,钟梅.基于IOWHA算子的对外直接投资组合预测[J].重庆工商大学学报(自然科学版),2016,33(3):76—81ZHANG X F,YANG G Y,ZHONG M. Outward Foreign Direct Investment Based on IOWHA Operator[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2016,33(3):76—81(in Chinese)
[8]江立辉,陈华友,丁芳清,等.基于IOWC-GOWA算子的区间组合预测模型[J].计算机工程与应用,2015,51(3):50—54JIANG L H,CHEN H Y,DING F Q,et al. Combination Forecasting Model Based on Induced Ordered Weighted Continuous Generalized Ordered Weighted Averaging Operator[J]. Computer Engineering and Applications,2015,51(3):50—54(in Chinese)
[9]曹晓俊,袁宏俊.连续区间广义有序加权调和平均算子及其在区间组合预测中应用[J].南京理工大学学报,2017,41(1):123—131CAO X J,YUAN H J. Continuous Generalized Ordered Weighted Harmonic Averaging Operator and Its Applications in Interval Combination Forecasting[J].Journal of Nanjing University of Science and Technology,2017,41(1):123—131(in Chinese)
[10]张超,袁宏俊.一类诱导广义有序加权对数的连续区间有序加权调和平均算子及其应用[J].延边大学学报(自然科学版),2017,43(4):302—307ZHANG C,YUAN H J. A Class of Induced Generalized Ordered Weighted Logarithmic Continuous Ordered Weighted Harmonic Averaging(IGOWLC-OWHA)Operators and Its Applications[J]. Journal of Yanbian University(Natural Science Edition),2017,43(4):302—307(in Chinese)
[11]袁宏俊,胡凌云.基于连续区间有序几何加权平均Power算子的区间型组合预测模型[J].数理统计与管理,2019(2):270—280YUAN H J, HU L Y. The Interval Combination Forecasting Model Based on COWG-WPA Operator[J].Journal of Applied Statistics and Management,2019(2):270—280(in Chinese)
[12]张进.不同精度准则下的区间型组合预测方法研究[D].合肥:安徽大学,2010ZHANG J. The Research of Interval Combination Forecasting Methods under Different Accuracy Criteria[D]. Hefei:Anhui University,2010(in Chinese)
[13]吴潜.基于中点及半径的区间数组合预测模型性质研究[J].统计与决策,2017,(4):36—40WU Q. The Nature of the Study of Interval Number Combination Forecast Model Based on Midpoints and Radius[J]. Statistics and Decision,2017(4):36—40(in Chinese)
[14]袁宏俊,钟梅,吴庆鹏.基于IGOWLA算子的区间组合预测模型[J].统计与决策,2016(14):22—25YUAN H J, ZHONG M, WU Q P. The Interval Combination Prediction Model Based on IGOWLA Operator[J]. Statistics and Decision,2016(14):22—25(in Chinese)
[15]袁宏俊,韦晨珺娃,钟梅.基于联系数贴近度的区间型组合预测模型及其有效性[J].统计与信息论坛,2017,32(6):31—37YUAN H J,WEI C J W,ZHONG M. Research on Interval Combination Forecasting Model and Its Effectiveness Based on Contact Number Degree[J].Statistics and Information Forum,2017,32(6):31—37(in Chinese)
[16]林义征,袁宏俊,宋马林.基于IOWHA算子与向量夹角余弦的联系数型区间组合预测[J].统计与决策,2016,449(5):84—86LIN Y Z, YUAN H J, SONG M L. The Interval Combination Prediction of Coefficient Type Based on IOWHA Operator and Vectorial Angle Cosine[J].Statistics and Decision, 2016, 449(5):84—86(in Chinese)
[17] YAGER R R. OWA Aggregation over a Continuous Interval Argument with Applications to Decision Making[J]. IEEE Transactions on Systems, Man, and Cybernetics,Part B,2004,34(5):1952—1963
[18] YAGER R R. Generalized OWA Aggregation Operators[J]. Fuzzy Optimization and Decision Making,2004,3(1):93—107
[19] ZHOU L G,CHEN H Y. Continuous Generalized OWA Operator and Its Application to Decision Making[J].Fuzzy Sets and Systems,2011,168(10):18—34
[20]陈华友,刘春林.基于IOWA算子组合预测方法[J].预测,2003,22(1):61—65CHENG H Y, LIU C L. A Kind of Combination Forecasting Method Based on Induced Ordered Weighted Averaging(IOWA)Operators[J]. Forecasting,2003,22(1):61—65(in Chinese)
[21]赵萌,邱菀华,刘北上.基于相对熵的多属性决策排列方法[J].控制与决策,2010,25(7):1098—1104ZHAO M, QIU W H, LIU B S. Relative Entropy Evaluation Method for Multiple Attribute Decision Making[J]. Control and Decision,2010,25(7):1098—1104(in Chinese)
[22]徐惠莉,吴柏林,江韶珊.区间时间序列预测准确度探讨[J].数量经济技术经济研究,2008,12(1):133—140XU H L, WU B L, JIANG Y S. On Forecasting Efficiency Evaluation for Interval Time Series[J]. The Journal of Quantitative and Technical Economics,2008,12(1):133—140(in Chinese)
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