一种基于IGOWMA算子和广义向量夹角余弦的最优区间组合预测模型

doi:10.12341/jssms22098

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (11): 3060-3072.DOI: 10.12341/jssms22098

• • 上一篇

一种基于IGOWMA算子和广义向量夹角余弦的最优区间组合预测模型

戴现朝^1,2, 李浩^1,2, 周礼刚^2,3, 徐鑫^2,3, 包恒嘉^2,3, 石学成^2,3

1. 安徽大学大数据与统计学院, 合肥 230601;
2. 安徽大学应用数学中心, 合肥 230601;
3. 安徽大学数学科学学院, 合肥 230601)

收稿日期:2022-02-15 修回日期:2022-05-10 发布日期:2022-12-13
通讯作者: 周礼刚, Email: lgzhou@ahu.edu.cn
基金资助:
国家自然科学基金(72171002, 71771001, 71701001, 71871001, 71901001, 71901088, 72071001, 72001001), 安徽省自然科学基金杰出青年基金(1908085J03), 安徽省学术和技术带头人及后备人选资助项目(2018H179), 安徽省高校学科(专业)拔尖人才学术资助项目(gxbjZD2020056), 安徽省自然科学基金(1808085QG211), 高校优秀青年人才支持计划项目(gxyq2019236), 安徽省高校人文社科基金重点项目 (SK2019A0013), 全国统计科学研究项目(2017LZ11), 国家级大学生创新创业训练项目(202110357010)资助课题.

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戴现朝, 李浩, 周礼刚, 徐鑫, 包恒嘉, 石学成. 一种基于IGOWMA算子和广义向量夹角余弦的最优区间组合预测模型[J]. 系统科学与数学, 2022, 42(11): 3060-3072.

Dai Xianchao, Li Hao, Zhou Ligang, Xu Xin, Bao Hengjia, Shi Xuecheng. An Optimal Interval Combination Forecasting Model Based on IGOWMA Operator and Generalized Vectorial Angle Cosine[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(11): 3060-3072.

An Optimal Interval Combination Forecasting Model Based on IGOWMA Operator and Generalized Vectorial Angle Cosine

Dai Xianchao^1,2, Li Hao^1,2, Zhou Ligang^2,3, Xu Xin^2,3, Bao Hengjia^2,3, Shi Xuecheng^2,3

1. School of Big Data and Statistics, Anhui University, Hefei 230601;
2. Anhui University Center for Applied Mathematics, Anhui University, Hefei 230601;
3. School of Mathematical Sciences, Anhui University, Hefei 230601

Received:2022-02-15 Revised:2022-05-10 Published:2022-12-13

文章提出一种基于IGOWMA算子和广义向量夹角余弦的最优区间组合预测模型.首先提出一种诱导广义有序加权多重平均(Induced generalized orderedweighted multiple averaging, IGOWMA)算子, 并研究其性质,其次以区间的中点和半径构造诱导变量,并分别构建基于IGOWMA算子和广义向量夹角余弦的区间中点和半径的最优组合预测模型,利用态度参数将其转化为单目标优化模型. 最后,通过实例分析验证所提出预测方法的合理性和有效性.

关键词： 区间预测, IGOWMA算子, 向量夹角余弦, 组合预测

This paper proposes an optimal interval combination forecasting model based on the IGOWMA operator and the generalized vectorial angle cosine. Firstly, an induced generalized ordered weighted multiple averaging (IGOWMA) operator is proposed, and its properties are investigated. Secondly, the induced variables are constructed with the midpoint and radius of the intervals, and the optimal combination forecasting models are put forward by using the midpoint and radius of intervals based on the IGOWMA operator and the generalized vectorial angle cosine respectively, and the attitude parameter is used to transform them into a single objective optimization model. Finally, the rationality and effectiveness of the proposed forecasting method are verified through an example.

Key words: Interval prediction, IGOWMA operator, vectorial angle cosine, combination forecasting

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[1] Bates J M, Granger C W J. The combination of forecasts. Operational Research Quarterly, 1969, 20(4): 451-468.
[2] Granger C W J, Ramanathan R. Improved methods of combining forecasts. International Journal of Forecasting, 1984, 3(2): 197-204.
[3] Clemen R T. Linear constrains and the efficiency of combined forecasts. Journal of Forecasting, 1986, 5(1): 31-38.
[4] 王应明, 傅国伟. 群组预测集结方法研究. 预测, 1993, 12(3): 42-45. (Wang Y M, Fu G W. Research on group prediction aggregation method. Forecasting, 1993, 12(3): 42-45.)
[5] 周传世. 非线性权组合预测模型及其最优权的确定. 预测, 1994, 13(2): 60-61, 64. (Zhou C S. Nonlinear weight combination prediction model and determination of its optimal weight. Forecasting, 1994, 13(2): 60-61, 64.)
[6] 傅庚, 唐小我, 曾勇. 广义递归方差倒数组合预测方法研究. 电子科技大学学报, 1995, 37(2): 211-217. (Fu G, Tang X W, Zeng Y. Research on generalized recursive reciprocal variance combination prediction method. Journal of University of Electronic Science and Technology, 1995, 37(2): 211-217.)
[7] 凌立文, 陈诗欣, 张大斌, 等. 基于多时间尺度组合策略的我国猪肉价格预测研究. 系统科学与数学, 2021, 41(10): 2829-2842. (Ling L W, Chen S X, Zhang D B, et al. A multi-time scales combination strategy for pork price forecasting. Journal of Systems Science and Mathematics Sciences, 2021, 41(10): 2829-2842.)
[8] Yager R R. On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man and Cybernetics, B, 1988, 18(1): 183-190.
[9] Yager R R, Filev D P. Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man and Cybernetics B, 1999, 29(2): 141-150.
[10 陈华友, 刘春林. 基于IOWA 算子的组合预测方法. 预测, 2003, 22(6): 61-65. (Chen H Y, Liu C L. A kind of combination forecasting method based on induced ordered weighted averaging (IOWA) operators. Forecasting, 2003, 22(6): 61-65.)
[11 凌立文, 张大斌. 组合预测模型构建方法及其应用研究综述. 统计与决策, 2019, 35(1): 18-23. (Ling L W, Zhang D B. A review of construction and application of combination forecast model. Statistics & Decision, 2019, 35(1): 18-23.)
[12 徐惠莉, 吴柏林, 江韶珊. 区间时间序列预测准确度探讨. 数量经济技术经济研究, 2008, 25(1): 133-140. (Xu H L, Wu B L, Jiang S S. On forecasting efficiency evaluation for interval time series. The Journal of Quantitative & Technical, 2008, 25(1): 133-140.)
[13 殷春武. 基于时间权重的区间型组合预测权重确定方法. 统计与决策, 2013, 29(21): 67-70. (Yin C W. Determination method of interval type combination forecast weight based on time weight. Statistics & Decision, 2013, 29(21): 67-70.)
[14 谭丹. 基于区间标度的旅游需求组合预测方法. 统计与决策, 2016, 32(15): 91-93. (Tan D. A forecasting method of tourism demand combination based on interval scaling. Statistics & Decision, 2016, 32(15): 91-93.)
[15 吴潜. 基于中点及半径的区间数组合预测模型性质研究. 统计与决策, 2017, 33(4): 36-40. (Wu Q. The nature of the study of interval number combination forecast model which based on midpoints and radius. Statistics & Decision, 2017, 33(4): 36-40.)
[16 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. 统计与信息论坛, 2017, 32(6): 31-37. (Yuan H J, Wei C J W, Zhong M. Research on interval combination forecasting model and its effectiveness based on contact number degree. Journal of Statistics and Information, 2017, 32(6): 31-37.)
[17 袁宏俊, 杜康, 胡凌云. 基于相对熵的最优区间型组合预测模型. 统计与决策, 2020, 36(11): 26-31. (Yuan H J, Du K, Hu L Y. Optimal interval combination forecasting model based on relative entropy. Statistics & Decision, 2020, 36(11): 26-31.)
[18 胡凌云, 袁宏俊, 李东勤. 一类区间型组合预测权重确定方法. 统计与决策, 2021, 37(11): 34-38. (Hu L Y, Yuan H J, Li D Q. A class of weight determination method for interval combination forecasting. Statistics & Decision, 2021, 37(11): 34-38.)
[19 王晓, 刘兮, 陈华友, 等. 基于IOWA 算子的区间组合预测方法. 武汉理工大学学报(信息与管理工程版), 2010, 32(2): 221-225. (Wang X, Liu X, Chen H Y, et al. An interval combinative forecasting method based on IOWA operators. Journal of Wuhan University of Technology $($Information & Management Engineering$)$, 2010, 32(2): 221-225.)
[20 陈华友, 李翔, 金磊, 等. 基于相关系数及IOWA 算子的区间组合预测方法. 统计与决策, 2012, 28(6): 83-86. (Chen H Y, Li X, Jin L, et al. Interval combination forecasting method based on correlation coefficient and IOWA operator. Statistics & Decision, 2012, 28(6): 83-86.)
[21 朱家明, 陈华友, 周礼刚, 等. 基于UWPA 算子的区间组合预测模型及其应用. 统计与决策, 2015, 31(19): 83-86. (Zhu J M, Chen H Y, Zhou L G, et al. Interval combination forecasting model based on UWPA operator and its application. Statistics & Decision, 2015, 31(19): 83-86.)
[22 沈永昌, 袁宏俊, 宋马林. ICOWA 算子的区间组合预测模型. 统计与决策, 2016, 32(17): 66-69. (Shen Y C, Yuan H J, Song M L. Interval combination forecasting model of ICOWA operator. Statistics & Decision, 2016, 32(17): 66-69.)
[23 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. 数理统计与管理, 2019, 38(2): 270-280. (Yuan H J, Hu L Y. Interval combination forecasting model based on continuous interval ordered geometric weighted average power operator. Journal of Applied Statistics and Management, 2019, 38(2): 270-280.)
[24 丁勤祥, 陶志富, 葛璐璐, 等. 基于L1范数的IOWGA算子的区间组合预测模型. 统计与决策, 2019, 35(22): 20-23. (Ding Q X, Tao Z F, Ge L L, et al. Interval combination forecasting model of IOWGA operators based on L1 norm. Statistics & Decision, 2019, 35(22): 20-23.)
[25 周代娣, 陈华友, 张倩昀, 等. 基于COWA 算子的相关性区间组合预测优化模型及其近似求解. 中国科学技术大学学报, 2020, 50(5): 673-681. (Zhou D D, Chen H Y, Zhang Q Y, et al. Optimization model of correlation interval combination forecasting based on COWA operator and its approximate solutions. Journal of University of Science and Technology, 2020, 50(5): 673-681.)
[26 谢小军, 马虹, 朱宁, 等. 基于区间相似度IOWGA算子的三角模糊数组合预测模型. 统计与决策, 2020, 36(23): 23-27. (Xie X J, Ma H, Zhu N, et al. A triangular fuzzy number combination forecasting model of IOWGA operator based on interval similarity. Statistics & Decision, 2020, 36(23): 23-27.)
[27 刘金培, 汪漂, 黄燕燕, 等. 基于区间时间序列小波多尺度分解的组合预测方法. 统计与决策, 2020, 36(19): 5-9. (Liu J P, Wang P, Huang Y Y, et al. Combined forecasting method based on interval times series wavelet multi-scale decomposition. Statistics & Decision, 2020, 36(19): 5-9.)
[28 刘金培, 罗瑞, 陈华友, 等. 非结构化数据驱动的混合二次分解汇率区间多尺度组合预测. 中国管理科学, 2021, 1-13, DOI: 10.16381/j.cnki.issn1003-207x.2021.0194. (Liu J P, Luo R, Chen H Y, et al. Unstructured data-driven multi-scale exchange rate interval combined forecasting based on hybrid secondary decomposition. Chinese Journal of Management Science, 2021, 1-13, DOI: 10.16381/j.cnki.issn1003-207x.2021.0194.)
[29 汪漂. 混合区间多尺度分解的区间时间序列组合预测. 运筹与管理, 2021, 30(10): 159-164. (Wang P. An interval time series combination forecasting approach based on hybird interval multi-scale decomposition. Operations Research and Management Science, 2021, 30(10): 159-164.)
[30 罗瑞, 刘金培, 陈华友, 等. 基于 LSTM-HFTS-EC 的PM2.5 区间多尺度组合预测研究. 重庆工商大学学报(自然科学版), 2022, 39(2): 59-67. (Luo R, Liu J P, Chen H Y, et al. Research on PM2.5 interval multi-scale combination prediction based on LSTM-HFTS-EC. Journal of Chongqing Technology and Business University $($Natural Science Edition), 2022, 39(2): 59-67.)
[31 张大斌, 李倩, 陈善盈, 等. 考虑协整的VECM-CoinSVR 区间预测组合模型. 系统工程理论与实践, 2021, 41(11): 3020-3030. (Zhang D B, Li Q, Chen S Y, et al. VECM-CoinSVR hybird model considering cointegration for interval-valued forecasting. Systems Engineering — Theory & Practice, 2021, 41(11): 3020-3030.)
[32 Zhou L G, Chen H Y, Liu J P. Generalized multiple averaging operators and their applications in group decision making. Group Decision and Negotiation, 2013, 22(2): 331-358.
[33 王应明. 基于相关性的组合预测方法研究. 预测, 2002, (2): 58-62. (Wang Y M. Research on the methods of combining forecasts based on correlativity. Forecasting, 2002, (2): 58-62.

[1]	凌立文, 陈诗欣, 张大斌, 张博婷. 基于多时间尺度组合策略的我国猪肉价格预测研究[J]. 系统科学与数学, 2021, 41(10): 2829-2842.
[2]	林鹏，倪璇，刘艳杰. 基于交叉验证方法的海洋经济发展的组合预测[J]. 系统科学与数学, 2018, 38(7): 823-829.
[3]	吴登生，李建平，孙晓蕾. 考虑模型相关性的组合预测过程中单项模型筛选研究[J]. 系统科学与数学, 2017, 37(2): 449-459.
[4]	刘秀丽，邹庆荣. 我国用水总量预测研究[J]. 系统科学与数学, 2016, 36(10): 1643-1651.
[5]	王川，赵俊晔，赵友森. 组合预测模型在农产品价格短期预测中的应用------以苹果为例的实证分析[J]. 系统科学与数学, 2013, 33(1): 89-96.

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