高阶直觉模糊时间序列预测模型

doi:10.11959/j.issn.1000-436x.2016099

摘要/Abstract

摘要：

提出一种高阶直觉模糊时间序列预测模型。模型首先应用模糊聚类算法实现论域的非等分划分；然后，针对直觉模糊时间序列的数据特性，提出一种更具客观性的直觉模糊集隶属度和非隶属度函数的确定方法；最后，利用直觉模糊多维取式推理建立高阶模型的预测规则，进行预测。在Alabama大学入学人数和北京市日均气温2组数据集上分别与典型方法进行对比实验，结果表明该模型有效提高了预测精度，证明了模型的有效性和优越性。

关键词: 高阶, 直觉模糊时间序列, 预测模型, 直觉模糊推理

Abstract:

A high order intuitionistic fuzzy time series forecasting model was built.In the new model,fuzzy clustering algorithm was used to get unequal intervals,and a more objective technique for ascertaining membership and non-membership functions of intuitionistic fuzzy set was proposed.On these bases,forecasting rules based on mul-ti-dimension intuitionistic fuzzy modus ponens inference were established.At last,contrast experiments on the enroll-ments of the university of Alabama and the daily average temperature of Beijing were carried out,which show that the novel model has a clear advantage of improving the forecasting accuracy.

Key words: high order, intuitionistic fuzzy time series, forecasting model, intuitionistic fuzzy inference

王亚男,雷英杰,雷阳,范晓诗. 高阶直觉模糊时间序列预测模型[J]. 通信学报, 2016, 37(5): 115-124.

Ya-nan WANG,Ying-jie LEI,Yang LEI,Xiao-shi FAN. High order intuitionistic fuzzy time series forecasting model[J]. Journal on Communications, 2016, 37(5): 115-124.

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参考文献 29

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直觉模糊集	c_μi	s_μi	c_?i	s_?i
A₁	13.154 5	0.009 9	13.154 5	0.033 5
A₂	13.795 5	0.098 3	13.795 5	0.331 8
A₃	14.601 5	0.042 4	14.601 5	0.143 1
A₄	15.553 5	0.166 2	15.553 5	0.560 8
A₅	16.392 0	0.017 6	16.392 0	0.059 5
A₆	17.066 5	0.091 2	17.066 5	0.307 7
A₇	18.047 5	0.109 1	18.047 5	0.368 2
A₈	18.854 5	0.036 0	18.854 5	0.121 6
A₉	19.574 5	0.075 2	19.574 5	0.253 8

年份	直觉模糊集	年份	直觉模糊集
1971	A₁	1982	A₄
1972	A₂	1983	A₄
1973	A₂	1984	A₄
1974	A₃	1985	A₄
1975	A₄	1986	A₄
1976	A₄	1987	A₆
1977	A₄	1988	A₇
1978	A₄	1989	A₈
1979	A₆	1990	A₉
1980	A₆	1991	A₉
1981	A₅

序号	直觉模糊逻辑关系
1	A₁ ,A₂ ,A₂→A₃
2	A₂ ,A₂ ,A₃→A₄
3	A₂ ,A₃ ,A₄→A₄
4	A₃ ,A₄ ,A₄→A₄
5	A₄ ,A₄ ,A₄→A₄
6	A₄ ,A₄ ,A₄→A₆
7	A₄ ,A₄ ,A₆→A₆
8	A₄ ,A₆ ,A₆→A₅
9	A₆ ,A₆ ,A₅→A₄
10	A₆ ,A₅ ,A₄→A₄
11	A₅ ,A₄ ,A₄→A₄
12	A₄ ,A₄ ,A₄→A₄
13	A₄ ,A₄ ,A₄→A₄
14	A₄ ,A₄ ,A₄→A₆
15	A₄ ,A₄ ,A₆→A₇
16	A₄ ,A₆ ,A₇→A₈
17	A₆ ,A₇ ,A₈→A₉
18	A₇ ,A₈ ,A₉→A₉

年份	实际招生数	预测值
1971	13 055	—
1972	13 563	—
1973	13 867	—
1974	14 696	14 233
1975	15 460	15 400
1976	15 311	15 420
1977	15 603	15 513
1978	15 861	15 605
1979	16 807	16 780
1980	16 919	17 010
1981	16 388	16 513
1982	15 433	15 605
1983	15 497	15 600
1984	15 145	15 221
1985	15 163	15 300
1986	15 984	15 853
1987	16 859	16 807
1988	18 150	17 545
1989	18 970	18 238
1990	19 328	18 780
1991	19 337	18 975
1992	18 876	18 880

指标	RMSE	AFE/%
文献[1]	677.1	3.35
文献[16]	433.6	2.56
文献[23]	418.9	2.07
文献[25]	399.3	1.99
本文	303.1	1.27