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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 77-90.doi: 10.6040/j.issn.1671-9352.4.2022.9449

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基于q-正交模糊集的冲突分析模型

林天泰(),杨斌*()   

  1. 西北农林科技大学理学院，陕西 杨凌 712100
  • 收稿日期:2022-08-09 出版日期:2023-12-20 发布日期:2023-12-19
  • 通讯作者: 杨斌 E-mail:tiantai_lin@163.com;binyang0906@nwsuaf.edu.cn
  • 作者简介:林天泰(1997—)，男，硕士研究生，研究方向为粗糙集、模糊集、冲突分析理论. E-mail: tiantai_lin@163.com
  • 基金资助:
    国家自然科学基金资助项目(12101500);中央高校基本科研业务经费资助项目(2452018054);中央高校基本科研业务经费资助项目(2452022370)

A q-rung orthopair fuzzy set based conflict analysis model

Tiantai LIN(),Bin YANG*()   

  1. School of Science, Northwest A&F University, Yangling 712100, Shaanxi, China
  • Received:2022-08-09 Online:2023-12-20 Published:2023-12-19
  • Contact: Bin YANG E-mail:tiantai_lin@163.com;binyang0906@nwsuaf.edu.cn

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摘要：

基于q-正交模糊集构建冲突分析模型，用q-正交模糊数表示对象关于议题的态度，并使用综合联盟距离衡量对象关于议题的联盟度，进一步通过分析对象和议题的3种联盟层次得到冲突的内因。其次，基于模糊粗糙自信息给出可行策略集的分类能力评价，由此构建寻找最佳可行策略的后向算法。模糊粗糙自信息所需的分类信息由对象的3种联盟层次充当，进一步便可定义联盟层次的上下近似，从而得到可行策略集的分类能力评价。最后，通过中东冲突的例子演示了模型及算法的可行性，并分析了阈值对输出的最佳可行策略集的影响。

关键词: 粗糙集, 自信息, 冲突分析, q-正交模糊集

Abstract:

We propose a q-rung orthopair fuzzy set based conflict analysis model, employ q-rung orthopair fuzzy numbers to denote the attitudes of agents toward issues. In addition, comprehensive alliance distance is used to measure the alliance degree of agents on the issues, and the conflicting reasons are obtained based on an analysis of the three alliance levels of agents and issues. Furthermore, the classification ability evaluation of a feasible strategy set is given based on fuzzy rough self-information, and a backward algorithm for finding the best feasible strategy is constructed. We consider the three alliance levels of the agents as the classification information required by fuzzy rough self-information. Further, the upper and lower approximations of the alliance levels can be defined, so as to obtain the classification ability evaluation of the feasible strategy set. Finally, the feasibility of the model and algorithm proposed in this paper is demonstrated through an example of Middle East conflict, and analyze the influence of changing value of thresholds on the optimal feasible strategy.

Key words: rough set, self-information, conflict analysis, q-rung orthopair fuzzy set

中图分类号: 

  • TP18

图1

q-正交模糊集"

表1

中东冲突的q-正交模糊冲突信息系统"

U c1 c2 c3 c4 c5
X1 Q(1.0，0.0) Q(0.9，0.3) Q(0.8，0.2) Q(0.9，0.1) Q(0.9，0.2)
X2 Q(0.9，0.1) Q(0.5，0.5) Q(0.1，0.9) Q(0.3，0.8) Q(0.1，0.9)
X3 Q(0.1，0.9) Q(0.1，0.9) Q(0.2，0.8) Q(0.1，0.9) Q(0.9，0.5)
X4 Q(0.7，0.7) Q(0.1，0.9) Q(0.3，0.7) Q(0.5，0.5) Q(0.1，0.9)
X5 Q(0.9，0.2) Q(0.4，0.6) Q(0.1，0.9) Q(0.1，0.9) Q(0.2，0.9)
X6 Q(0.0，1.0) Q(0.9，0.1) Q(0.2，0.9) Q(0.5，0.5) Q(0.8，0.4)

表2

对象和议题的3种联盟层次"

q $ \mathscr{S} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ $ \mathscr{W} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ $ \mathscr{N} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ $ \mathscr{S} \mathscr{A}_{A}^{c_{\diamond}, c^{\diamond}}$ $ \mathscr{W} \mathscr{A}_{A}^{c_{\diamond}, c^{\diamond}}$
3 {x2，x4，x5} {x1，x3} {x6} {c3} {c4，c5}
4 {x2，x5} {x1，x3，x4} {x6} {c3} {c4，c5}
5 {x2，x5} {x1，x3，x4} {x6} {c3} {c4，c5}

表3

中东冲突可行策略"

B1 B2 B3 B4 B5 B6
{c1} {c1，c2} {c2，c4} {c1，c2，c3} {c1，c4，c5} {c1，c2，c3，c4}
B7 B8 B9 B10 B11 B12
{c2} {c1，c3} {c2，c5} {c1，c2，c4} {c2，c3，c4} {c1，c2，c3，c5}
B13 B14 B15 B16 B17 B18
{c3} {c1，c4} {c3，c4} {c1，c2，c5} {c2，c3，c5} {c1，c2，c4，c5}
B19 B20 B21 B22 B23 B24
{c4} {c1，c5} {c3，c5} {c1，c3，c4} {c2，c4，c5} {c1，c3，c4，c5}
B25 B26 B27 B28 B29 B30
{c5} {c2，c3} {c4，c5} {c1，c3，c5} {c3，c4，c5} {c2，c3，c4，c5}

表4

中东冲突可行策略的自信息"

q I(B1) I(B2) I(B3) I(B4) I(B5) I(B6)
3 0.765 4 1.740 2 0.502 0 1.746 4 1.575 6 1.799 9
4 0.645 9 1.465 0 0.242 3 1.515 0 1.431 8 1.569 3
5 0.697 0 1.457 5 0.240 4 1.510 4 1.476 4 1.572 7
q I(B7) I(B8) I(B9) I(B10) I(B11) I(B12)
3 0.247 2 0.957 6 0.455 8 1.799 9 0.611 5 1.764 5
4 0.073 0 0.825 0 0.197 7 1.569 3 0.328 2 1.529 1
5 0.066 0 0.854 8 0.143 4 1.572 7 0.304 9 1.523 3
q I(B13) I(B14) I(B15) I(B16) I(B17) I(B18)
3 1.339 1 1.282 9 0.137 7 1.764 5 0.581 7 1.818 1
4 2.177 4 1.265 9 0.085 3 1.520 9 0.310 3 1.583 5
5 1.977 0 1.380 2 0.110 2 1.506 2 0.247 4 1.585 7
q I(B19) I(B20) I(B21) I(B22) I(B23) I(B24)
3 0.203 4 1.340 9 0.127 1 1.282 9 0.643 2 1.575 6
4 0.131 5 1.166 1 0.120 8 1.265 9 0.354 3 1.431 8
5 0.125 8 1.163 9 0.101 0 1.380 2 0.318 4 1.476 4
q I(B25) I(B26) I(B27) I(B28) I(B29) I(B30)
3 0.724 9 0.509 3 0.280 5 1.340 9 0.390 3 0.688 3
4 0.210 4 0.236 9 0.201 5 1.173 8 0.269 3 0.395 8
5 0.228 5 0.191 3 0.221 0 1.190 6 0.267 8 0.359 6

表5

最佳可行策略关于c°的变化情况"

c° $ \mathscr{S} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ $ \mathscr{W} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ $ \mathscr{N} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ OFS
0.50 {x2，x4，x5} $ \emptyset $ {x1，x3，x6} {c1，c2，c4}
0.51 {x2，x4，x5} $ \emptyset $ {x1，x3，x6} {c1，c2，c4}
0.52 {x2，x5} {x4} {x1，x3，x6} {c1，c2，c4，c5}
0.53 {x2，x5} {x4} {x1，x3，x6} {c1，c2，c4，c5}
0.54 {x2，x5} {x4} {x1，x3，x6} {c1，c2，c4，c5}
0.55 $ \emptyset $ {x2，x4，x5} {x1，x3，x6} {c1，c2，c4}

表6

最佳可行策略关于c°的变化情况"

c° $ \mathscr{S} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ $ \mathscr{W} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ $ \mathscr{N} \mathscr{U}_{A}^{c_{\circ}, c^{\circ}}$ OFS
0.5 {x2，x4，x5} $ \emptyset $ {x1，x3，x6} {c1，c2，c4}
0.4 {x2，x4，x5} {x1，x3} {x6} {c1，c2，c4，c5}
0.3 {x2，x4，x5} {x1，x3，x6} $ \emptyset $ {c1，c2，c4}
0.2 {x2，x4，x5} {x1，x3，x6} $ \emptyset $ {c1，c2，c4}
0.1 {x2，x4，x5} {x1，x3，x6} $ \emptyset $ {c1，c2，c4}
0.0 {x2，x4，x5} {x1，x3，x6} $ \emptyset $ {c1，c2，c4}
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