基于模糊影响图和前景理论的重大疫情防控策略决策方法

doi:10.16381/j.cnki.issn1003-207x.2022.1030

Abstract

Abstract:

In order to minimize the impact of major epidemic on economic development， and balance the relationship between major epidemic prevention and control and economic development， a decision-making method of major epidemic prevention and control strategy is proposed， which is constructed by fuzzy influence diagrams and prospect theory. Considering that the decision-making of major epidemic prevention and control strategies is characterized by reference dependence， loss avoidance and probability judgment distortion， the prospect theory is used to make the decision of alternative strategies. In order to solve the problem that it is difficult to select specific reference points to evaluate the impact of prevention and control strategies on economic development， "before the implementation of prevention and control strategies" is selected as the psychological reference point for decision-makers， and the fuzzy influence diagrams are used to analyze the fuzzy influence relationship of prevention and control strategies on economic development. Fuzzy inference and fuzzy synthesis are used to evaluate the profit and loss of economic development brought by the prevention and control strategy and its probability distribution. Finally， the prospect theory parameters obtained from the experiments in China and the United States are compared by examples. The results show that the same optimal prevention and control strategy could be obtained regardless of the experimental parameters in the United States or in China， and the optimal prevention and control strategy is not sensitive to the loss avoidance coefficient λ. However， the suboptimal prevention and control strategy is sensitive to loss aversion coefficient λ， especially when λ=2.25， which requires decision makers to make careful decisions. If the decision maker is sensitive to the loss， it is recommended to adopt the experimental parameters in China.

Key words: major epidemic, prevention and control strategy, fuzzy influence diagram, prospect theory, decision-making method

CLC Number:

C934

Zhipeng Chang, Zhiying Wang, Wenhe Chen. Decision Making Method of Major Epidemic Prevention and Control Strategy Based on Fuzzy Influence Diagrams and Prospect Theory[J]. Chinese Journal of Management Science, 2025, 33(6): 171-181.

Figures/Tables 23

防控策略	$△ x 1$	$△ x 2$	$⋯$	$△ x J$
$A 1$	$p 11$	$p 12$	$⋯$	$p 1 J$
$A 2$	$p 21$	$p 22$	$⋯$	$p 2 J$
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
$A D$	$p D 1$	$p D 2$	$⋯$	$p D J$

防控策略	$Θ 1$	$Θ 2$	$Θ 3$
$A 1$	$ξ 3$	$ξ 3$	$ξ 4$
$A 2$	$ξ 2$	$ξ 5$	$ξ 4$
$A 3$	$ξ 1$	$ξ 2$	$ξ 3$

$A 1 → Y 1$	$i f A 1 = Θ 1$	$t h e n Y 1 = Ω 0$
	$e l s e i f A 1 = Θ 2$	$t h e n Y 1 = Ω 0$
	$e l s e i f A 1 = Θ 3$	$t h e n Y 1 = Ω - 1$
$A 1 → Y 2$	$i f A 1 = Θ 1$	$t h e n Y 2 = Ω 0$
	$e l s e i f A 1 = Θ 2$	$t h e n Y 2 = Ω 0$
	$e l s e i f A 1 = Θ 3$	$t h e n Y 2 = Ω 1$
$A 1 → Y 3$	$i f A 1 = Θ 1$	$t h e n Y 3 = Ω - 1$
	$e l s e i f A 1 = Θ 2$	$t h e n Y 3 = Ω - 2$
	$e l s e i f A 1 = Θ 3$	$t h e n Y 3 = Ω - 2$
$A 1 → Y 4$	$i f A 1 = Θ 1$	$t h e n Y 4 = Ω 1$
	$e l s e i f A 1 = Θ 2$	$t h e n Y 4 = Ω 1$
	$e l s e i f A 1 = Θ 3$	$t h e n Y 4 = Ω 1$
$A 1 → Y 5$	$i f A 1 = Θ 1$	$t h e n Y 5 = Ω - 1$
	$e l s e i f A 1 = Θ 2$	$t h e n Y 5 = Ω - 1$
	$e l s e i f A 1 = Θ 3$	$t h e n Y 5 = Ω - 2$

$A 2 → Y 1$	$i f A 2 = Θ 1$	$t h e n Y 1 = Ω - 1$
	$e l s e i f A 2 = Θ 2$	$t h e n Y 1 = Ω - 2$
	$e l s e i f A 2 = Θ 3$	$t h e n Y 1 = Ω - 3$
$A 2 → Y 2$	$i f A 2 = Θ 1$	$t h e n Y 2 = Ω 0$
	$e l s e i f A 2 = Θ 2$	$t h e n Y 2 = Ω 1$
	$e l s e i f A 2 = Θ 3$	$t h e n Y 2 = Ω 2$
$A 2 → Y 3$	$i f A 2 = Θ 1$	$t h e n Y 3 = Ω - 1$
	$e l s e i f A 2 = Θ 2$	$t h e n Y 3 = Ω - 1$
	$e l s e i f A 2 = Θ 3$	$t h e n Y 3 = Ω - 2$
$A 2 → Y 4$	$i f A 2 = Θ 1$	$t h e n Y 4 = Ω 1$
	$e l s e i f A 2 = Θ 2$	$t h e n Y 4 = Ω 2$
	$e l s e i f A 2 = Θ 3$	$t h e n Y 4 = Ω 3$
$A 2 → Y 5$	$i f A 2 = Θ 1$	$t h e n Y 5 = Ω 0$
	$e l s e i f A 2 = Θ 2$	$t h e n Y 5 = Ω - 2$
	$e l s e i f A 2 = Θ 3$	$t h e n Y 5 = Ω - 3$

$A 3 → Y 1$	$i f A 3 = Θ 1$	$t h e n Y 1 = Ω 0$
	$e l s e i f A 3 = Θ 2$	$t h e n Y 1 = Ω - 1$
	$e l s e i f A 3 = Θ 3$	$t h e n Y 1 = Ω - 1$
$A 3 → Y 2$	$i f A 3 = Θ 1$	$t h e n Y 2 = Ω 0$
	$e l s e i f A 3 = Θ 2$	$t h e n Y 2 = Ω - 1$
	$e l s e i f A 3 = Θ 3$	$t h e n Y 2 = Ω - 3$
$A 3 → Y 3$	$i f A 3 = Θ 1$	$t h e n Y 3 = Ω - 2$
	$e l s e i f A 3 = Θ 2$	$t h e n Y 3 = Ω - 2$
	$e l s e i f A 3 = Θ 3$	$t h e n Y 3 = Ω - 3$
$A 3 → Y 4$	$i f A 3 = Θ 1$	$t h e n Y 4 = Ω 0$
	$e l s e i f A 3 = Θ 2$	$t h e n Y 4 = Ω 0$
	$e l s e i f A 3 = Θ 3$	$t h e n Y 4 = Ω 0$
$A 3 → Y 5$	$i f A 3 = Θ 1$	$t h e n Y 5 = Ω 0$
	$e l s e i f A 3 = Θ 2$	$t h e n Y 5 = Ω - 1$
	$e l s e i f A 3 = Θ 3$	$t h e n Y 5 = Ω - 2$

$Y 1 → G D P$	$i f Y 1 = Ω - 3$ $t h e n G D P = Ω - 3$	$e l s e i f Y 1 = Ω - 2$ $t h e n G D P = Ω - 2$	$e l s e i f Y 1 = Ω - 1$ $t h e n G D P = Ω - 1$
	$e l s e i f Y 1 = Ω 0$ $t h e n G D P = Ω 0$	$e l s e i f Y 1 = Ω 1$ $t h e n G D P = Ω 1$	$e l s e i f Y 1 = Ω 2$ $t h e n G D P = Ω 2$
	$e l s e i f Y 1 = Ω 3$ $t h e n G D P = Ω 3$
$Y 2 → G D P$	$i f Y 2 = Ω - 3$ $t h e n G D P = Ω - 2$	$e l s e i f Y 2 = Ω - 2$ $t h e n G D P = Ω - 1$	$e l s e i f Y 2 = Ω - 1$ $t h e n G D P = Ω 0$
	$e l s e i f Y 2 = Ω 0$ $t h e n G D P = Ω 0$	$e l s e i f Y 2 = Ω 1$ $t h e n G D P = Ω 1$	$e l s e i f Y 2 = Ω 2$ $t h e n G D P = Ω 2$
	$e l s e i f Y 2 = Ω 3$ $t h e n G D P = Ω 2$
$Y 3 → G D P$	$i f Y 3 = Ω - 3$ $t h e n G D P = Ω - 1$	$e l s e i f Y 3 = Ω - 2$ $t h e n G D P = Ω - 1$	$e l s e i f Y 3 = Ω - 1$ $t h e n G D P = Ω 0$
	$e l s e i f Y 3 = Ω 0$ $t h e n G D P = Ω 0$	$e l s e i f Y 3 = Ω 1$ $t h e n G D P = Ω 2$	$e l s e i f Y 3 = Ω 2$ $t h e n G D P = Ω 2$
	$e l s e i f Y 3 = Ω 3$ $t h e n G D P = Ω 3$
$Y 4 → G D P$	$i f Y 4 = Ω - 3$ $t h e n G D P = Ω - 3$	$e l s e i f Y 4 = Ω - 2$ $t h e n G D P = Ω - 2$	$e l s e i f Y 4 = Ω - 1$ $t h e n G D P = Ω - 1$
	$e l s e i f Y 4 = Ω 0$ $t h e n G D P = Ω 0$	$e l s e i f Y 4 = Ω 1$ $t h e n G D P = Ω 2$	$e l s e i f Y 4 = Ω 2$ $t h e n G D P = Ω 3$
	$e l s e i f Y 4 = Ω 3$ $t h e n G D P = Ω 3$
$Y 5 → G D P$	$i f Y 5 = Ω - 3$ $t h e n G D P = Ω - 2$	$e l s e i f Y 5 = Ω - 2$ $t h e n G D P = Ω - 1$	$e l s e i f Y 5 = Ω - 1$ $t h e n G D P = Ω 0$
	$e l s e i f Y 5 = Ω 0$ $t h e n G D P = Ω 0$	$e l s e i f Y 5 = Ω 1$ $t h e n G D P = Ω 0$	$e l s e i f Y 5 = Ω 2$ $t h e n G D P = Ω 0$
	$e l s e i f Y 5 = Ω 3$ $t h e n G D P = Ω 1$

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0	0	0	0	0	0	0	0	0	0	0	0
0.1	0	0	0	0	0	0	0	0	0	0	0	0
0.2	0	0	0	0	0	0	0	0	0	0	0	0
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.5	0.2	0.5	0.5	0.5	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.1
0.6	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.2	0.6	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.6	0.4	6.5
0.9	0.2	0.6	0.6	0.6	0.8	0.9	0.8	0.8	0.9	0.6	0.4	7.2
1.0	0.2	0.6	0.6	0.6	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.4

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0.6	0.6	0.7	0.7	0.8	1	0.8	0.8	1	0.7	0.7	8.4
0.1	0.6	0.6	0.7	0.7	0.8	0.9	0.8	0.8	0.9	0.7	0.7	8.2
0.2	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	7.5
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0	0	0	0	0	0	0	0	0	0	0	0
0.5	0	0	0	0	0	0	0	0	0	0	0	0
0.6	0	0	0	0	0	0	0	0	0	0	0	0
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.7	0.7	0.7	0.7	0.7	0.7	0.5	0.7	0.7	0.7	0.7	7.5
0.9	0.9	0.9	0.9	0.8	0.8	0.9	0.8	0.8	0.9	0.9	0.9	9.5
1.0	1	0.9	1	0.8	0.8	1	0.8	0.8	1	0.9	1	10

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	$Σ$
0.0	0.2	0.5	0.5	0.5	0.8	1	0.8	0.8	1	0.6	6.7
0.1	0.2	0.5	0.5	0.5	0.8	0.9	0.8	0.8	0.9	0.6	6.5
0.2	0.2	0.5	0.5	0.5	0.7	0.7	0.7	0.7	0.7	0.6	5.8
0.3	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.5	0.2	0.6	1	0.8	0.8	1	0.8	0.8	1	0.6	7.6
0.6	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.7	0	0	0	0	0	0	0	0	0	0	0
0.8	0	0	0	0	0	0	0	0	0	0	0
0.9	0	0	0	0	0	0	0	0	0	0	0
1.0	0	0	0	0	0	0	0	0	0	0	0

△GDP	$A 1$	$A 2$	$A 3$
-5%	0.0270	0.1000	0.0286
-4%	0.0811	0.0900	0.0857
-3%	0.0811	0.1000	0.1143
-2%	0.0811	0.0800	0.1143
-1%	0.1081	0.0800	0.1143
0%	0.1351	0.1000	0.1143
1%	0.1081	0.0800	0.1143
2%	0.1081	0.0800	0.1143
3%	0.1351	0.1000	0.1143
4%	0.0811	0.0900	0.0857
5%	0.0541	0.1000	0.0000

实验	$α$	$β$	$λ$	$γ$	$δ$
美国	0.88	0.88	2.25	0.61	0.69
中国	1.21	1.02	2.25	0.55	0.49

△GDP	美国实验参数			中国实验参数
△GDP	$A 1$	$A 2$	$A 3$	$A 1$	$A 2$	$A 3$
-5%	0.0756	0.1701	0.0784	0.1265	0.1976	0.1292
-4%	0.1499	0.1597	0.155	0.1848	0.1911	0.1881
-3%	0.1499	0.1701	0.1843	0.1848	0.1976	0.2062
-2%	0.1499	0.1487	0.1843	0.1848	0.1840	0.2062
-1%	0.1783	0.1487	0.1843	0.2026	0.1840	0.2062
0%	0.2037	0.1701	0.1843	0.2174	0.1976	0.2062
1%	0.1935	0.1669	0.1989	0.2010	0.1777	0.2055
2%	0.1935	0.1669	0.1989	0.2010	0.1777	0.2055
3%	0.2157	0.1863	0.1989	0.2198	0.1947	0.2055
4%	0.1680	0.1769	0.1727	0.1787	0.1865	0.1828
5%	0.1370	0.1863	0.0000	0.1509	0.1947	0.0000

实验	$A 1$	$A 2$	$A 3$	排序
美国	-0.0261	-0.0421	-0.0435	$A 1 ≻ A 2 ≻ A 3$
中国	-0.0391	-0.0469	-0.0461	$A 1 ≻ A 3 ≻ A 2$

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符号	名称	含义
○	随机节点	不确定事件或随机变量
◎	确定节点	确定事件或变量
◇	价值节点	所研究问题的目标函数或变量
→	关联弧	随机节点进入随机节点或价值节点的有向弧

△GDP	美国实验参数	中国实验参数
-5%	-0.1612	-0.1060
-4%	-0.1324	-0.0844
-3%	-0.1028	-0.0629
-2%	-0.0720	-0.0416
-1%	-0.0391	-0.0205
0%	0.0000	0.0000
1%	0.0174	0.0038
2%	0.0320	0.0088
3%	0.0457	0.0144
4%	0.0589	0.0203
5%	0.0716	0.0267

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Decision Making Method of Major Epidemic Prevention and Control Strategy Based on Fuzzy Influence Diagrams and Prospect Theory

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△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0	0	0	0	0	0	0	0	0	0	0	0
0.1	0	0	0	0	0	0	0	0	0	0	0	0
0.2	0	0	0	0	0	0	0	0	0	0	0	0
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.5	0.2	0.5	0.5	0.5	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.1
0.6	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.2	0.6	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.6	0.4	6.5
0.9	0.2	0.6	0.6	0.6	0.8	0.9	0.8	0.8	0.9	0.6	0.4	7.2
1.0	0.2	0.6	0.6	0.6	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.4

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0.6	0.6	0.7	0.7	0.8	1	0.8	0.8	1	0.7	0.7	8.4
0.1	0.6	0.6	0.7	0.7	0.8	0.9	0.8	0.8	0.9	0.7	0.7	8.2
0.2	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	7.5
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0	0	0	0	0	0	0	0	0	0	0	0
0.5	0	0	0	0	0	0	0	0	0	0	0	0
0.6	0	0	0	0	0	0	0	0	0	0	0	0
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.7	0.7	0.7	0.7	0.7	0.7	0.5	0.7	0.7	0.7	0.7	7.5
0.9	0.9	0.9	0.9	0.8	0.8	0.9	0.8	0.8	0.9	0.9	0.9	9.5
1.0	1	0.9	1	0.8	0.8	1	0.8	0.8	1	0.9	1	10

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	$Σ$
0.0	0.2	0.5	0.5	0.5	0.8	1	0.8	0.8	1	0.6	6.7
0.1	0.2	0.5	0.5	0.5	0.8	0.9	0.8	0.8	0.9	0.6	6.5
0.2	0.2	0.5	0.5	0.5	0.7	0.7	0.7	0.7	0.7	0.6	5.8
0.3	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.5	0.2	0.6	1	0.8	0.8	1	0.8	0.8	1	0.6	7.6
0.6	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.7	0	0	0	0	0	0	0	0	0	0	0
0.8	0	0	0	0	0	0	0	0	0	0	0
0.9	0	0	0	0	0	0	0	0	0	0	0
1.0	0	0	0	0	0	0	0	0	0	0	0

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0	0	0	0	0	0	0	0	0	0	0	0
0.1	0	0	0	0	0	0	0	0	0	0	0	0
0.2	0	0	0	0	0	0	0	0	0	0	0	0
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.5	0.2	0.5	0.5	0.5	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.1
0.6	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.2	0.6	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.6	0.4	6.5
0.9	0.2	0.6	0.6	0.6	0.8	0.9	0.8	0.8	0.9	0.6	0.4	7.2
1.0	0.2	0.6	0.6	0.6	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.4

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0.6	0.6	0.7	0.7	0.8	1	0.8	0.8	1	0.7	0.7	8.4
0.1	0.6	0.6	0.7	0.7	0.8	0.9	0.8	0.8	0.9	0.7	0.7	8.2
0.2	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	7.5
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0	0	0	0	0	0	0	0	0	0	0	0
0.5	0	0	0	0	0	0	0	0	0	0	0	0
0.6	0	0	0	0	0	0	0	0	0	0	0	0
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.7	0.7	0.7	0.7	0.7	0.7	0.5	0.7	0.7	0.7	0.7	7.5
0.9	0.9	0.9	0.9	0.8	0.8	0.9	0.8	0.8	0.9	0.9	0.9	9.5
1.0	1	0.9	1	0.8	0.8	1	0.8	0.8	1	0.9	1	10

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	$Σ$
0.0	0.2	0.5	0.5	0.5	0.8	1	0.8	0.8	1	0.6	6.7
0.1	0.2	0.5	0.5	0.5	0.8	0.9	0.8	0.8	0.9	0.6	6.5
0.2	0.2	0.5	0.5	0.5	0.7	0.7	0.7	0.7	0.7	0.6	5.8
0.3	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.5	0.2	0.6	1	0.8	0.8	1	0.8	0.8	1	0.6	7.6
0.6	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.7	0	0	0	0	0	0	0	0	0	0	0
0.8	0	0	0	0	0	0	0	0	0	0	0
0.9	0	0	0	0	0	0	0	0	0	0	0
1.0	0	0	0	0	0	0	0	0	0	0	0

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0	0	0	0	0	0	0	0	0	0	0	0
0.1	0	0	0	0	0	0	0	0	0	0	0	0
0.2	0	0	0	0	0	0	0	0	0	0	0	0
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.5	0.2	0.5	0.5	0.5	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.1
0.6	0.2	0.5	0.5	0.5	0.8	0.8	0.8	0.8	0.8	0.6	0.4	6.7
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.2	0.6	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.6	0.4	6.5
0.9	0.2	0.6	0.6	0.6	0.8	0.9	0.8	0.8	0.9	0.6	0.4	7.2
1.0	0.2	0.6	0.6	0.6	0.8	1.0	0.8	0.8	1.0	0.6	0.4	7.4

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	5%	$Σ$
0.0	0.6	0.6	0.7	0.7	0.8	1	0.8	0.8	1	0.7	0.7	8.4
0.1	0.6	0.6	0.7	0.7	0.8	0.9	0.8	0.8	0.9	0.7	0.7	8.2
0.2	0.6	0.6	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	7.5
0.3	0	0	0	0	0	0	0	0	0	0	0	0
0.4	0	0	0	0	0	0	0	0	0	0	0	0
0.5	0	0	0	0	0	0	0	0	0	0	0	0
0.6	0	0	0	0	0	0	0	0	0	0	0	0
0.7	0	0	0	0	0	0	0	0	0	0	0	0
0.8	0.7	0.7	0.7	0.7	0.7	0.7	0.5	0.7	0.7	0.7	0.7	7.5
0.9	0.9	0.9	0.9	0.8	0.8	0.9	0.8	0.8	0.9	0.9	0.9	9.5
1.0	1	0.9	1	0.8	0.8	1	0.8	0.8	1	0.9	1	10

△GDP频率	-5%	-4%	-3%	-2%	-1%	0%	1%	2%	3%	4%	$Σ$
0.0	0.2	0.5	0.5	0.5	0.8	1	0.8	0.8	1	0.6	6.7
0.1	0.2	0.5	0.5	0.5	0.8	0.9	0.8	0.8	0.9	0.6	6.5
0.2	0.2	0.5	0.5	0.5	0.7	0.7	0.7	0.7	0.7	0.6	5.8
0.3	0	0	0	0	0	0	0	0	0	0	0
0.4	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.5	0.2	0.6	1	0.8	0.8	1	0.8	0.8	1	0.6	7.6
0.6	0.2	0.6	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.6	7
0.7	0	0	0	0	0	0	0	0	0	0	0
0.8	0	0	0	0	0	0	0	0	0	0	0
0.9	0	0	0	0	0	0	0	0	0	0	0
1.0	0	0	0	0	0	0	0	0	0	0	0