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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (7): 67-79.doi: 10.6040/j.issn.1671-9352.4.2022.9768

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可拓序贯三支决策模型及应用

王君宇1,2,3(),杨亚锋1,2,3,薛静轩1,李丽红1,2,3,*()   

  1. 1. 华北理工大学理学院, 河北 唐山 063210
    2. 河北省数据科学与应用重点实验室, 河北 唐山 063210
    3. 唐山市工程计算重点实验室, 河北 唐山 063210
  • 收稿日期:2022-08-09 出版日期:2023-07-20 发布日期:2023-07-05
  • 通讯作者: 李丽红 E-mail:1784557362@qq.com;22687426@qq.com
  • 作者简介:王君宇(1996—), 女, 硕士研究生, 研究方向为数据挖掘、三支决策等. E-mail: 1784557362@qq.com
  • 基金资助:
    河北省数据科学与应用重点实验室项目(10120201);唐山市数据科学重点实验室项目(10120301)

Extension sequential three-way decision model and its application

Junyu WANG1,2,3(),Yafeng YANG1,2,3,Jingxuan XUE1,Lihong LI1,2,3,*()   

  1. 1. College of Science, North China University of Science and Technology, Tangshan 063210, Hebei, China
    2. Hebei Province Key Laboratory of Data Science and Application, Tangshan 063210, Hebei, China
    3. Tangshan Key Laboratory of Engineering Computing, Tangshan 063210, Hebei, China
  • Received:2022-08-09 Online:2023-07-20 Published:2023-07-05
  • Contact: Lihong LI E-mail:1784557362@qq.com;22687426@qq.com

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摘要：

将可拓评价基本方法与“三分而治”决策思想融合, 引入序贯思想, 构建可拓序贯三支决策模型, 实现动态决策与挖掘优化指标的目的。首先, 对数据进行标准化处理, 计算属性的权重; 其次, 将可拓评价方法作为三支决策的评价准则, 定义新的决策规则, 阐释划分3个域的合理性; 然后, 根据属性权重得到多个粒度的序贯评价属性, 进行多阶段三支决策, 给出决策结果; 最后, 根据决策结果对引起样本划分变化的指标进行分析, 并提出优化建议。将模型应用于水资源承载力分析领域, 与熵权物元可拓决策模型进行对比。结果表明, 运用可拓序贯三支决策模型与熵权物元可拓决策模型所得的评价结果基本一致, 准确率达84.55%, 验证了模型的有效性和实用性。

关键词: 序贯三支决策, 可拓评价, 粒化, 水资源承载力

Abstract:

The basic method of extension evaluation and the "rule by three divisions" decision-making idea are integrated, and the sequential idea is introduced to construct an extension sequential three-way decision model and realize the purpose of dynamic decision-making and mining optimization indicators. Firstly, the data is standardized and the weight of attributes is calculated. The extension evaluation method is used as the evaluation criterion of the three-way decisions, new decision rules are defined, and the rationality of dividing the three domains is explained. Then, according to the attribute weight, the sequential evaluation attributes of multiple granularity are obtained, the multi-stage three-way decision is made, and the decision results are given. Finally, according to the decision-making results, the indicators that cause changes in sample division are analyzed, and optimization suggestions are put forward. The model was applied to the analysis of water resources carrying capacity, and compared with the entropy weight matter-element extension decision-making model. The results show that the evaluation results obtained by using the extension sequential three-way decision model and the entropy weight matter-element extension decision-making model are basically consistent, the accuracy rate reaches 84.55%, which verifies the validity and practicability of the model.

Key words: sequential three-way decision, extension evaluation, granulation, carrying capacity of water resource

中图分类号: 

  • TP181

图1

三支决策框架图"

表1

长江经济带水资源承载力评价等级及标准"

评价指标 性质 评价等级及标准值
Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ
人均水资源量/m3 正 80~500 500~1 000 1 000~2 000 2 000~3 000 3 000~5 500
农业用水占比/% 负 60~100 55~60 50~55 30~50 0~30
生活用水占比/% 正 0~4 4~5 5~7 7~10 10~100
人均库容量/m3 正 0~200 200~400 400~600 600~800 800~2 200
生态环境用水占比/% 正 0~1 1~2 2~3 3~5 5~10
污水处理率/% 正 0~40 40~50 50~80 80~95 95~100
万元GDP化学需氧量排放量/kg 负 3~7 2~3 1~2 0.5~1 0~0.5
建成区绿化覆盖率/% 正 0~20 20~30 30~35 35~40 40~50
森林覆盖率/% 正 0~10 10~20 20~40 40~50 50~100
湿地总面积占国土面积比重/% 正 0~2 2~4 4~6 6~8 8~74
造林面积/hm2 正 0~60 000 60 000~170 000 170 000~280 000 280 000~480 000 480 000~720 000
第一产业占GDP比值/% 负 20~15 13~15 10~13 5~10 0~5
第二产业占GDP比值/% 负 52~56 48~52 44~48 40~44 0~40
农业灌溉亩均用水量/m3 负 800~1 000 600~800 400~600 200~400 0~200

表2

各指标权重"

符号指标权重
c1 湿地总面积占国土面积比重/% 0.099 0
c2 森林覆盖率/% 0.093 7
c3 造林面积/hm2 0.092 4
c4 生活用水占比/% 0.087 6
c5 农业用水占比/% 0.087 1
c6 人均库容量/m3 0.083 7
c7 第一产业占GDP比值/% 0.082 2
c8 万元GDP化学需氧量排放量/kg 0.075 5
c9 人均水资源量/m3 0.072 9
c10 第二产业占GDP比值/% 0.064 8
c11 生态环境用水占比/% 0.057 5
c12 农业灌溉亩均用水量/m3 0.052 9
c13 污水处理率/% 0.026 4
c14 建成区绿化覆盖率/% 0.024 3

表3

2018年长江经济带水资源承载力指标与等级的关联度"

省级行政区 评价指标 关联度
K1(x0) K2(x0) K3(x0) K4(x0) K5(x0)
上海 c1 -0.989 9 -0.989 6 -0.989 3 -0.988 9 0.011 1
c2 -0.223 5 0.404 0 -0.298 0 -0.649 0 -0.719 2
江苏 c1 -0.481 1 -0.460 8 -0.438 8 -0.414 9 0.295 6
c2 -0.254 9 0.480 0 -0.240 0 -0.620 0 -0.696 0
浙江 c1 -0.449 5 -0.387 8 -0.310 4 -0.210 6 0.044 1
c2 -0.549 2 -0.492 9 -0.323 8 -0.188 6 0.188 6
安徽 c1 -0.422 6 -0.316 8 -0.163 7 0.270 0 -0.067 5
c2 -0.394 3 -0.231 9 0.432 5 -0.283 8 -0.427 0
江西 c1 -0.387 6 -0.210 1 0.275 0 -0.091 7 -0.318 8
c2 -0.568 4 -0.514 5 -0.352 7 -0.223 2 0.223 2
湖北 c1 -0.426 1 -0.326 7 -0.185 5 0.115 0 -0.028 8
c2 -0.427 8 -0.331 1 0.019 5 -0.009 8 -0.207 8
湖南 c1 -0.368 8 -0.144 1 0.405 0 -0.198 3 -0.398 8
c2 -0.444 1 -0.374 0 -0.163 2 0.031 0 -0.006 2
重庆 c1 -0.168 9 0.255 0 -0.372 5 -0.581 7 -0.686 3
c2 -0.434 4 -0.349 0 -0.067 3 0.311 0 -0.137 8
四川 c1 -0.308 4 0.195 0 -0.097 5 -0.398 3 -0.548 8
c2 -0.424 3 -0.321 6 0.098 5 -0.049 3 -0.239 4
贵州 c1 0.405 0 -0.405 0 -0.702 5 -0.801 7 -0.851 3
c2 -0.435 5 -0.351 9 -0.079 3 0.377 0 -0.124 6
云南 c1 0.285 0 -0.285 0 -0.642 5 -0.761 7 -0.821 3
c2 -0.500 4 -0.438 0 -0.250 7 -0.100 8 0.100 8

表4

2009—2018年上海水资源承载力指标与等级的关联度"

年份 评价指标 关联度
K1(x0) K2(x0) K3(x0) K4(x0) K5(x0)
2009 c1 -0.717 8 -0.709 7 -0.701 2 -0.692 1 0.307 9
c2 0.059 0 -0.059 0 -0.529 5 -0.764 8 -0.811 8
2010 c1 -0.717 8 -0.709 7 -0.701 2 -0.692 1 0.307 9
c2 0.059 0 -0.059 0 -0.529 5 -0.764 8 -0.811 8
2011 c1 -0.717 8 -0.709 7 -0.701 2 -0.692 1 0.307 9
c2 0.059 0 -0.059 0 -0.529 5 -0.764 8 -0.811 8
2012 c1 -0.717 8 -0.709 7 -0.701 2 -0.692 1 0.307 9
c2 0.059 0 -0.059 0 -0.529 5 -0.764 8 -0.811 8
2013 c1 -0.989 9 -0.989 6 -0.989 3 -0.988 9 0.011 1
c2 -0.064 5 0.074 0 -0.463 0 -0.731 5 -0.785 2
2014 c1 -0.989 9 -0.989 6 -0.989 3 -0.988 9 0.011 1
c2 -0.064 5 0.074 0 -0.463 0 -0.731 5 -0.785 2
2015 c1 -0.989 9 -0.989 6 -0.989 3 -0.988 9 0.011 1
c2 -0.064 5 0.074 0 -0.463 0 -0.731 5 -0.785 2
2016 c1 -0.989 9 -0.989 6 -0.989 3 -0.988 9 0.011 1
c2 -0.064 5 0.074 0 -0.463 0 -0.731 5 -0.785 2
2017 c1 -0.989 9 -0.989 6 -0.989 3 -0.988 9 0.011 1
c2 -0.064 5 0.074 0 -0.463 0 -0.731 5 -0.785 2
2018 c1 -0.989 9 -0.989 6 -0.989 3 -0.988 9 0.011 1
c2 -0.223 5 0.404 0 -0.298 0 -0.649 0 -0.719 2

表5

2018年长江经济带水资源承载力评价值"

省级行政区 综合关联度 等级
K1(xi) K2(xi) K3(xi) K4(xi) K5(xi)
上海 -0.617 2 -0.312 0 -0.653 2 -0.823 7 -0.344 0 Ⅱ
江苏 -0.371 1 -0.003 4 -0.342 1 -0.514 6 -0.186 5 Ⅱ
浙江 -0.498 0 -0.438 9 -0.316 9 -0.199 9 0.114 4 Ⅴ
安徽 -0.408 8 -0.275 5 0.126 2 0.000 8 -0.242 3 Ⅲ
江西 -0.475 6 -0.358 1 -0.030 2 -0.155 6 -0.055 2 Ⅲ
湖北 -0.426 9 -0.328 9 -0.085 8 0.054 3 -0.115 8 Ⅳ
湖南 -0.405 4 -0.255 9 0.128 7 -0.086 8 -0.207 9 Ⅲ
重庆 -0.298 0 -0.038 7 -0.224 1 -0.147 6 -0.419 6 Ⅱ
四川 -0.364 8 -0.056 2 -0.002 2 -0.228 6 -0.398 3 Ⅲ
贵州 -0.003 7 -0.379 2 -0.399 5 -0.228 6 -0.497 9 Ⅰ
云南 -0.096 9 -0.359 4 -0.452 0 -0.440 3 -0.372 9 Ⅰ

表6

2009—2018年上海水资源承载力评价值"

年份 综合关联度 等级
K1(xi) K2(xi) K3(xi) K4(xi) K5(xi)
2009 -0.340 1 -0.393 3 -0.617 7 -0.727 4 -0.236 5 Ⅴ
2010 -0.340 1 -0.393 3 -0.617 7 -0.727 4 -0.236 5 Ⅴ
2011 -0.340 1 -0.393 3 -0.617 7 -0.727 4 -0.236 5 Ⅴ
2012 -0.340 1 -0.393 3 -0.617 7 -0.727 4 -0.236 5 Ⅴ
2013 -0.539 9 -0.472 4 -0.733 4 -0.863 8 -0.376 1 Ⅴ
2014 -0.539 9 -0.472 4 -0.733 4 -0.863 8 -0.376 1 Ⅴ
2015 -0.539 9 -0.472 4 -0.733 4 -0.863 8 -0.376 1 Ⅴ
2016 -0.539 9 -0.472 4 -0.733 4 -0.863 8 -0.376 1 Ⅴ
2017 -0.539 9 -0.472 4 -0.733 4 -0.863 8 -0.376 1 Ⅴ
2018 -0.617 2 -0.312 0 -0.653 2 -0.823 7 -0.344 0 Ⅱ

图2

第一次水资源承载力决策结果"

图3

第二次水资源承载力决策结果"

图4

第三次水资源承载力决策结果"

图5

第四次水资源承载力决策结果"

图6

第五次水资源承载力决策结果"

图7

第六次水资源承载力决策结果"

图8

第七次水资源承载力决策结果"

图9

决策结果对比"

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