模糊智能决策树模型与应用研究

doi:10.3778/j.issn.1673-9418.2009051

计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (3): 703-712.DOI: 10.3778/j.issn.1673-9418.2009051

• 理论与算法 • 上一篇

模糊智能决策树模型与应用研究

鱼先锋¹^,²^,⁺(), 耿生玲¹

1.青海师范大学计算机科学学院,西宁 810008
2.商洛学院数学与计算机应用学院,陕西商洛 726000

收稿日期:2020-09-14 修回日期:2020-11-17 出版日期:2022-03-01 发布日期:2020-11-25
通讯作者: + E-mail: pioneer.369@163.com
作者简介:鱼先锋（1984—）,男,讲师,CCF会员,主要研究方向为模糊系统分析、模型检测。
耿生玲（1970—）,女,教授,CCF高级会员, 主要研究方向为不确定信息智能处理技术和理论。
基金资助:
国家自然科学基金(61862055);陕西省重点研发计划项目(2022GY-073)

Fuzzy Intelligent Decision Tree Model and Its Application

YU Xianfeng¹^,²^,⁺(), GENG Shengling¹

1. School of Computer Science, Qinghai Normal University, Xining 810008, China
2. Institute of Mathematics and Computer Application, Shangluo University, Shangluo, Shaanxi 726000, China

Received:2020-09-14 Revised:2020-11-17 Online:2022-03-01 Published:2020-11-25
About author:YU Xianfeng, born in 1984, lecturer, member of CCF. His research interests include fuzzy system analysis and model checking.
GENG Shengling, born in 1970, professor, senior member of CCF. Her research interests include uncertain information intelligent processing technology and theory.
Supported by:
National Natural Science Foundation of China(61862055);Key Research and Development Program of Shaanxi Province(2022GY-073)

摘要/Abstract

摘要：

决策问题是计算智能最核心的问题之一。基于模糊数学理论建立了一个普适的模糊决策树模型;用节点刻画决策前提和控制信息,用树上的边形式化推理规则;并在节点和边上定义合理的模糊决策算子,进行多级综合决策。工程决策考虑不同方案的成本、可行性和收益,将这些信息进行融合作为决策方案优劣的测度;建立加权模糊智能决策模型,并给出了基于该模型求最优的多属性受限决策的算法。讨论了模型和算法的复杂度。通过两个应用实例验证说明了决策模型和最优决策方案求解算法考虑定性与定量信息,决策结果科学合理且信息量大。

关键词: 模糊决策树, 受限决策, 最优决策, 加权函数

Abstract:

Decision making is one of the core problems of computational intelligence. Based on the theory of fuzzy mathematics, a general fuzzy decision tree model is established. The nodes are used to describe the decision premise and control information, and the edges of the tree are used to formalize the reasoning rules. The reasonable fuzzy decision operators are defined on the nodes and the edges to make a multi-level comprehensive decision. Engineering decisions consider the costs, feasibility, and benefits of different options. The fusion of these information is used to measure the merits and demerits of decision making schemes. The weighted fuzzy intelligent decision-making model is established, and the algorithm of multi-attribute constrained decision-making based on the model is given. The complexity of the model and algorithm is discussed. Finally, through two application examples, it is proven that the decision model and the algorithm of optimal decision scheme consider qualitative and quantitative information, and the decision result is scientific and reasonable with large amount of information.

Key words: fuzzy decision tree, limited decision, optimal decision, weighting function

中图分类号:

TP301.2

鱼先锋, 耿生玲. 模糊智能决策树模型与应用研究[J]. 计算机科学与探索, 2022, 16(3): 703-712.

YU Xianfeng, GENG Shengling. Fuzzy Intelligent Decision Tree Model and Its Application[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(3): 703-712.

图/表 10

图1 模糊智能决策树框架示意图

Fig.1 Frame diagram of fuzzy intelligent decision tree

图2 污泥含量对各等级的隶属度曲线

Fig.2 Membership curve of sludge content to each grade

图3 油脂含量对各等级的隶属度曲线

Fig.3 Membership curve of grease content to each grade

表1 模糊合成推理规则库

Table 1 Rule base of fuzzy synthetic reasoning

污泥	油脂
污泥	SZ	MZ	LZ
SN	TVS(1)	TM(2)	TL(3)
MN	TM(4)	TM(5)	TL(6)
LN	TL(7)	TL(8)	TVL(9)

图4 TM(4)对应的决策子树

Fig.4 Decision tree corresponding to TM (4)

表2 被激活规则

Table 2 Activated rules

污泥	油脂
污泥	SZ	MZ
MN	TM(4)	TM(5)
LN	TL(7)	TL(8)

表3 洗涤等级的特征函数

Table 3 Characteristic function of washing grade

时长等级	洗涤时长/min
TVS	5
TS	18
TM	32
TL	50
TVL	80

表4 不同水平下4个阶段完成所需时间

Table 4 Time required for completion of 4 stages at different levels

水平	阶段
水平	$S 1$	$S 2$	$S 3$	$S 4$
$α$	6个月	5个月	8个月	4个月
$β$	4个月	3个月	5个月	2个月
$γ$	2个月	2个月	3个月	4个月

表4 不同水平下4个阶段完成所需时间

Table 4 Time required for completion of 4 stages at different levels

水平	阶段
水平	$S 1$	$S 2$	$S 3$	$S 4$
$α$	6个月	5个月	8个月	4个月
$β$	4个月	3个月	5个月	2个月
$γ$	2个月	2个月	3个月	4个月

表5 不同水平下各阶段预计费用

Table 5 Estimated cost of each stage at different levels

水平	阶段
水平	$S 1$	$S 2$	$S 3$	$S 4$
$α$	300	400	600	180
$β$	600	600	900	300
$γ$	900	900	1 200	600

表5 不同水平下各阶段预计费用

Table 5 Estimated cost of each stage at different levels

水平	阶段
水平	$S 1$	$S 2$	$S 3$	$S 4$
$α$	300	400	600	180
$β$	600	600	900	300
$γ$	900	900	1 200	600

表6 不同水平下各阶段完成可能性

Table 6 Completion possibility of each stage under different levels

水平	阶段
水平	$S 1$	$S 2$	$S 3$	$S 4$
$α$	1.00	1.00	1.00	1.00
$β$	0.85	0.70	0.80	0.80
$γ$	0.80	0.55	0.65	0.76

表6 不同水平下各阶段完成可能性

Table 6 Completion possibility of each stage under different levels

水平	阶段
水平	$S 1$	$S 2$	$S 3$	$S 4$
$α$	1.00	1.00	1.00	1.00
$β$	0.85	0.70	0.80	0.80
$γ$	0.80	0.55	0.65	0.76

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模糊智能决策树模型与应用研究

Fuzzy Intelligent Decision Tree Model and Its Application

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