JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 91-107.doi: 10.6040/j.issn.1671-9352.4.2022.7001

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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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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

CLC Number: 

  • O225

Table 1

A probabilistic multi-valued information system"

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

Table 2

Value table of EB(a)"

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

Table 3

Value table of Ci1(a, b)"

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

Table 4

Value table of Ci2(a, b)"

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

Table 5

Value table of Ci3(a, b)"

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

Table 6

Value table of Ci1, i2(a, b)"

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

Table 7

Value table of Ci1, i3(a, b)"

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

Table 8

Value table of Ci2, i3(a, b)"

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

Table 9

Value table of Ci1, i2, i3(a, b)"

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

Table 10

Table of allianceclassALβα(a, B)"

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}

Table 11

Table of neutralclass NEβα(a, B)"

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 $

Table 12

Table ofconflictclass COβα(a, B)"

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 $

Table 13

Value table of CJ(a, b)"

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

Table 14

Value table of $ C_{\mathscr{P}(I)}$(a, b)"

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

Table 15

Value table of E′B(a)"

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

Table 16

Value table of σB(a)"

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

Table 17

Value table of σ′B(a)"

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

Table 18

A probabilistic multi-valued information system"

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

Fig.1

Curves of the change of |ALβα(A, $ \mathscr{P}(I)$)| with β under different conflict degree definitions"

Fig.2

Curves of the change of |COβα(A, $ \mathscr{P}(I)$)| with α under different conflict degree definitions"

Table 19

Comparison of the existing conflict analysis papers"

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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[8] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[9] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[10] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
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