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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 91-107.doi: 10.6040/j.issn.1671-9352.4.2022.7001

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基于概率多值信息系统的冲突分析和决策分析

金雷1(),冯涛1,*(),张少谱2   

  1. 1. 河北科技大学理学院，河北 石家庄 050018
    2. 石家庄铁道大学数理系，河北 石家庄 050043
  • 收稿日期:2022-07-26 出版日期:2023-12-20 发布日期:2023-12-19
  • 通讯作者: 冯涛 E-mail:jinlei_97@163.com;fengtao_new@163.com
  • 作者简介:金雷(1997—)，男，硕士研究生，研究方向为粗糙集、模糊集理论，粒计算等. E-mail: jinlei_97@163.com
  • 基金资助:
    国家自然科学基金资助项目(62076088);河北省自然科学基金资助项目(A2020208004);河北省自然科学基金资助项目(A2021210027);河北省教育厅基金资助项目(QN2019062);河北省教育厅基金资助项目(QN2020196)

Conflict analyses and deciosion analyses based on probabilistic multi-valued information systems

Lei JIN1(),Tao FENG1,*(),Shaopu ZHANG2   

  1. 1. School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, Hebei, China
    2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, Hebei, China
  • Received:2022-07-26 Online:2023-12-20 Published:2023-12-19
  • Contact: Tao FENG E-mail:jinlei_97@163.com;fengtao_new@163.com

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摘要：

在多值信息系统的基础上加入了概率度量，提出了概率多值信息系统；在概率多值信息系统中，使用Bregman散度对代理间的冲突度进行了定义，并以此得到各代理的联合类、中立类和冲突类；最后通过代理对问题集取值结果的均值和标准差，给出了一种概率多值信息系统中可行决策集的获取方法。

关键词: 冲突分析, 概率多值信息系统, 信息提取

Abstract:

A probabilistic multi-valued information system is proposed by adding a probability measure to the multi-valued information system. In addition, in a probabilistic multi-valued information system, the degree of conflict between agents is defined by Bregman divergence, and the alliance class, neutral class and conflict class of each agent are obtained. Finally, a method for obtaining feasible decision sets in probabilistic multi-valued information systems is proposed based on the mean value and standard deviation of the evaluation results.

Key words: conflict analysis, probabilistic multi-valued information system, information extraction

中图分类号: 

  • O225

表1

概率多值信息系统"

A $ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 -0.5/0.3 0.7/0.8 0.4/0.5 0.1/0.24 -0.8/0.4 0.3/0.4 0.4/1.0
-0.2/0.6 -0.1/0.2 -0.7/0.4 -0.3/0.06 -0.5/0.5 -0.7/0.3
0.4/0.1 -0.1/0.1 0.25/0.48 1.0/0.1 -1.0/0.3
-0.15/0.12
0.55/0.08
0.15/0.02
a2 0.2/0.8 0.8/0.3 0.7/1.0 0.5/0.24 -0.8/0.7 0.9/1.0 0.7/0.3
-0.1/0.2 -1.0/0.7 -0.4/0.56 0.1/0.3 0.4/0.7
0.35/0.06
-0.55/0.14
a3 0.9/1.0 0.6/1.0 -0.7/0.6 0.75/1.0 -0.7/0.7 -0.8/1.0 1.0/1.0
0.4/0.4 -0.9/0.3
a4 1.0/1.0 0.8/1.0 -0.3/1.0 0.9/1.0 -0.9/1.0 -0.4/1.0 0.6/1.0

表2

EB(a)数值表"

A $ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 -0.23 0.54 -0.09 0.155 -0.47 -0.39 0.40
a2 0.14 -0.46 0.70 -0.160 -0.53 0.90 0.49
a3 0.90 0.60 -0.26 0.750 -0.76 -0.80 1.00
a4 1.00 0.80 -0.30 0.900 -0.90 -0.40 0.60

表3

Ci1(a, b)数值表"

A A
a1 a2 a3 a4
a1 0.000 0 0.037 6 0.309 3 0.375 0
a2 0.037 6 0.000 0 0.144 8 0.190 8
a3 0.309 3 0.144 8 0.000 0 0.003 2
a4 0.375 0 0.190 8 0.003 2 0.000 0

表4

Ci2(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.313 2 0.012 8 0.029 6
a2 0.313 2 0.000 0 0.330 5 0.445 2
a3 0.012 8 0.330 5 0.000 0 0.010 7
a4 0.029 6 0.445 2 0.010 7 0.000 0

表5

Ci3(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.172 2 0.068 1 0.039 2
a2 0.172 2 0.000 0 0.240 9 0.226 2
a3 0.068 1 0.240 9 0.000 0 0.032 6
a4 0.039 2 0.226 2 0.032 6 0.000 0

表6

Ci1, i2(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.044 5 0.088 8 0.1425
a2 0.044 5 0.000 0 0.209 1 0.286 6
a3 0.088 8 0.209 1 0.000 0 0.006 5
a4 0.142 5 0.286 6 0.006 5 0.000 0

表7

Ci1, i3(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.050 8 0.052 6 0.079 2
a2 0.050 8 0.000 0 0.034 9 0.057 1
a3 0.052 6 0.034 9 0.000 0 0.006 9
a4 0.079 2 0.057 1 0.006 9 0.000 0

表8

Ci2, i3(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.429 9 0.081 0 0.038 4
a2 0.429 9 0.000 0 0.692 4 0.397 5
a3 0.081 0 0.692 4 0.000 0 0.040 6
a4 0.038 4 0.397 5 0.040 6 0.000 0

表9

Ci1, i2, i3(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.004 2 0.097 6 0.009 6
a2 0.004 2 0.000 0 0.074 5 0.005 3
a3 0.097 6 0.074 5 0.000 0 0.004 6
a4 0.009 6 0.005 3 0.004 6 0.000 0

表10

联合类ALβα(a, B)表"

A$ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 {a1, a2} {a1, a3, a4} {a1, a3, a4} {a1, a2, a3} {a1, a2, a3, a4} {a1, a3, a4} {a1, a2, a3, a4}
a2 {a1, a2} {a2} {a2} {a1, a2} {a1, a2, a3, a4} {a2} {a1, a2, a3, a4}
a3 {a3, a4} {a1, a3, a4} {a1, a3, a4} {a1, a3, a4} {a1, a2, a3, a4} {a1, a3, a4} {a1, a2, a3, a4}
a4 {a3, a4} {a1, a3, a4} {a1, a3, a4} {a3, a4} {a1, a2, a3, a4} {a1, a3, a4} {a1, a2, a3, a4}

表11

中立类NEβα(a, B)表"

A$ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 $ \emptyset $ $ \emptyset $ {a2} {a4} $ \emptyset $ $ \emptyset $ $ \emptyset $
a2 {a3, a4} $ \emptyset $ {a1, a3, a4} {a3, a4} $ \emptyset $ $ \emptyset $ $ \emptyset $
a3 {a2} $ \emptyset $ {a2} {a2} $ \emptyset $ $ \emptyset $ $ \emptyset $
a4 {a2} $ \emptyset $ {a2} {a1, a2} $ \emptyset $ $ \emptyset $ $ \emptyset $

表12

冲突类COβα(a, B)表"

A$ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 {a3, a4} {a2} $ \emptyset $ $ \emptyset $ $ \emptyset $ {a2} $ \emptyset $
a2 $ \emptyset $ {a1, a3, a4} $ \emptyset $ $ \emptyset $ $ \emptyset $ {a1, a3, a4} $ \emptyset $
a3 {a1} {a2} $ \emptyset $ $ \emptyset $ $ \emptyset $ {a2} $ \emptyset $
a4 {a1} {a2} $ \emptyset $ $ \emptyset $ $ \emptyset $ {a2} $ \emptyset $

表13

CJ(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.260 3 0.134 4 0.147 7
a2 0.260 3 0.000 0 0.389 2 0.344 5
a3 0.134 4 0.389 2 0.000 0 0.018 2
a4 0.147 7 0.344 5 0.018 2 0.000 0

表14

$ C_{\mathscr{P}(I)}$(a, b)数值表"

AA
a1 a2 a3 a4
a1 0.000 0 0.150 3 0.101 4 0.101 9
a2 0.150 3 0.000 0 0.246 7 0.229 8
a3 0.101 4 0.246 7 0.000 0 0.020 9
a4 0.101 9 0.229 8 0.020 9 0.000 0

表15

E′B(a)数值表"

A$ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 0.437 630 0.385 804 0.000 470 0.411 717 -0.661 354 -0.192 905 0.618 090
a2 0.412 889 0..316 305 0.058 290 0.364 597 -0.650 733 -0.101 409 0.606 339
a3 0.489 651 0..419 174 -0.029 553 0.454 412 -0.678 269 -0.237 990 0.637 849
a4 0.489 651 0.419 174 -0.029 553 0.454 412 -0.678 269 -0.237 990 0.637 849
A 0.457 217 0.384 377 0.000 704 0.420 797 -0.667 192 -0.190 676 0.624 295

表16

σB(a)数值表"

A$ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 0.249 199 0.320 000 0.518 556 0.202 793 0.510 000 0.575 239 0.000 000
a2 0.120 000 0.824 864 0.000 000 0.416 773 0.412 432 0.000 000 0.137 477
a3 0.000 000 0.000 000 0.538 888 0.000 000 0.091 652 0.000 000 0.000 000
a4 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000 0.000 000

表17

σ′B(a)数值表"

A$ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 0.096 306 0.279 970 0.275 014 0.152 733 0.258 559 0.157 761 0.032 028
a2 0.098 346 0..325 144 0.250 962 0.174 638 0.271 201 0.144 896 0.040 748
a3 0.086 565 0..250 319 0.276 744 0.136 650 0.237 017 0.142 356 0.028 515
a4 0.086 698 0.252 974 0.272 340 0.137 940 0.237 268 0.141 637 0.029 024
A 0.091 979 0.277 102 0.268 765 0.150 490 0.251 011 0.146 663 0.032 579

表18

概率多值信息系统"

A$ \mathscr{P}(I)$
i1 i2 i3 i1, i2 i1, i3 i2, i3 i1, i2, i3
a1 0.7/1.0 -0.9/1.0 -0.7/1.0 -0.8/1.0 0.4/1.0 -0.8/1.0 0.2/1.0
a2 0.15/0.8 -0.9/0.7 0.7/1.0 0.5/0.4 -0.15/0.4 -0.1/0.7 0.45/0.7
-0.8/0.2 0.1/0.2 -0.35/0.3 0.3/0.4 0.4/0.2 0.75/0.3
0.3/0.1 0.1/0.3 -0.4/0.2 0.5/0.1
a3 -0.95/1.0 0.5/1.0 -0.7/0.6 0.85/1.0 -0.9/0.8 -0.1/0.6 -0.8/1.0
0.4/0.4 -0.3/0.2 0.45/0.4
a4 1.0/1.0 -0.8/0.7 -0.3/1.0 0.7/1.0 0.95/1.0 -0.55/0.7 -0.9/1.0
-1.0/0.3 -0.65/0.3
a5 0.8/0.6 0.7/0.5 -1.0/0.7 -0.3/0.3 0.6/0.5 -0.15/0.35 1.0/0.8
0.5/0.3 0.3/0.5 -0.7/0.3 -0.6/0.3 0.4/0.5 0.0/0.15 0.75/0.2
-0.2/0.1 0.2/0.3 -0.35/0.35
-0.2/0.15
a6 0.15/1.0 0.9/1.0 0.6/0.5 -0.9/1.0 0.4/1.0 0.75/0.5 0.8/0.9
0.9/0.5 0.9/0.5 -1.0/0.1
a7 0.45/1.0 0.6/1.0 0.8/0.6 -1.0/1.0 1.0/1.0 0.7/0.6 0.3/1.0
-0.3/0.4 0.15/0.4
a8 -1.0/1.0 0.4/1.0 -0.3/1.0 0.8/1.0 -0.9/1.0 0.05/1.0 0.55/1.0
a9 -0.2/1.0 -1.0/1.0 0.9/1.0 -0.1/1.0 0.3/1.0 -0.05/1.0 -0.75/1.0
a10 -0.65/1.0 0.95/1.0 0.75/1.0 0.85/1.0 0.6/1.0 0.85/1.0 0.95/1.0

图1

不同冲突度定义下|ALβα(A, $ \mathscr{P}(I)$)|随β的变化曲线"

图2

不同冲突度定义下|COβα(A, $ \mathscr{P}(I)$)|随α的变化曲线"

表19

现有冲突分析文章对比"

来源 信息系统 二元关系 决策选择 主要工作
Pawlak[1-3] 三值信息系统 √ × 在三值信息系统中建立了冲突分析的基本框架
Liu[8] 直觉模糊信息系统 √ × 在直觉模糊信息系统中给出了一种冲突度的定义，并以此确定了各代理的冲突类、中立类和联合类
Lang[12] 动态三值信息系统 √ × 在动态三值信息系统中给出一种冲突度定义，并将冲突分析与决策理论粗糙集相结合，给出三支冲突分析模型
Sun[9] 三值信息系统 × √ 针对冲突问题的解决首次给出了方案(仅选择代理集“支持”和“反对”的问题)
Sun[10] 三值信息系统 × √ 结合决策理论粗糙集给出了一种冲突问题的解决思路，将代理集支持的问题集和反对的问题集作为可以实行的策略集合，解决冲突问题(仅选择代理集“支持”和“反对”的问题)
Lang[5] 毕达哥拉斯模糊信息系统 √ × 在毕达哥拉斯模糊信息系统中给出冲突度的定义，并结合多属性群决策的方法给出了一种毕达哥拉斯模糊信息系统中的冲突分析模型
Lang[13] 三值信息系统 × √ 将粗糙集理论和形式概念分析下冲突问题的决策选择模型进行了统一(仅选择代理集“支持”的问题)
Yi[7] 犹豫模糊信息系统 √ × 在犹豫模糊信息系统中给出一种冲突度的定义，并对冲突问题产生的原因进行讨论
Suo[15] 不完备的三值信息系统；不完备的多值信息系统 √ × 分别在不完备的三值信息系统和多值信息系统中给出2种冲突度的定义，并以此确定各代理的冲突类、中立类和联合类
Lang[14] 三值信息系统；多值信息系统 √ × 使用标准化的曼哈顿距离作为Pawlak和Yao的定义的冲突度的推广，给出冲突度和联合度2个度量的公理化定义
Xu[23] 三值信息系统；模糊信息系统 × √ 定义了代理集的一致性度量，并以此进行决策选择(代理集“支持”、“中立”和“反对”的问题都可以被选出)
Li[6] 三角模糊信息系统 √ × 在三角模糊信息系统中定义冲突度
Du[17] 毕达哥拉斯模糊信息系统 √ √ 在毕达哥拉斯模糊信息系统上定义2种全新的冲突度；在问题集上定义冲突度，并使用其给出一种决策选择模型(代理集“支持”、“中立”和“反对”的问题都可以被选出
本文 概率多值信息系统 √ √ 提出了概率多值信息系统，在概率多值信息系统上定义冲突度，根据评价结果的均值、标准差及平均冲突度进行了决策选择(仅选择代理集“支持”的问题)
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[1] 林天泰,杨斌. 基于q-正交模糊集的冲突分析模型[J]. 《山东大学学报(理学版)》, 2023, 58(12): 77-90.
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