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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}
1 PAWLAK Z . On conflicts[J]. International Journal of Man-Machine Studies, 1984, 21 (2): 127- 134.
doi: 10.1016/S0020-7373(84)80062-0
2 DEJA R . Conflict analysis[J]. International Journal of Intelligent Systems, 2002, 17 (2): 235- 253.
doi: 10.1002/int.10019
3 PAWLAK Z . An inquiry into anatomy of conflicts[J]. Information Sciences, 1998, 109 (1/2/3/4): 65- 78.
4 PAWLAK Z . Some remarks on conflict analysis[J]. European Journal of Operational Research, 2005, 166 (3): 649- 654.
doi: 10.1016/j.ejor.2003.09.038
5 PAWLAK Z , SKOWRON A . Rough sets and Boolean reasoning[J]. Information Sciences, 2007, 177 (1): 41- 73.
doi: 10.1016/j.ins.2006.06.007
6 LI X , WANG X , LANG G , et al. Conflict analysis based on three-way decision for triangular fuzzy information systems[J]. International Journal of Approximate Reasoning, 2021, 132, 88- 106.
doi: 10.1016/j.ijar.2020.12.004
7 LIU Y , LIN Y . Intuitionistic fuzzy rough set model based on conflict distance and applications[J]. Applied Soft Computing, 2015, 31, 266- 273.
doi: 10.1016/j.asoc.2015.02.045
8 LANG G , MIAO D , FUJITA H . Three-way group conflict analysis based on Pythagorean fuzzy set theory[J]. IEEE Transactions on Fuzzy Systems, 2019, 28 (3): 447- 461.
9 TONG S , SUN B , CHU X , et al. Trust recommendation mechanism-based consensus model for Pawlak conflict analysis decision making[J]. International Journal of Approximate Reasoning, 2021, 135, 91- 109.
doi: 10.1016/j.ijar.2021.05.001
10 YI H , ZHANG H , LI X , et al. Three-way conflict analysis based on hesitant fuzzy information systems[J]. International Journal of Approximate Reasoning, 2021, 139, 12- 27.
doi: 10.1016/j.ijar.2021.09.002
11 LANG G , MIAO D , CAI M . Three-way decision approaches to conflict analysis using decision-theoretic rough set theory[J]. Information Sciences, 2017, 406, 185- 207.
12 SUN B , MA W . Rough approximation of a preference relation by multi-decision dominance for a multi-agent conflict analysisproblem[J]. Information Sciences, 2015, 315, 39- 53.
doi: 10.1016/j.ins.2015.03.061
13 YAO Y . Three-way conflict analysis: reformulations and extensions of the Pawlak model[J]. Knowledge-Based Systems, 2019, 180, 26- 37.
doi: 10.1016/j.knosys.2019.05.016
14 SUN B , MA W , ZHAO H . Rough set-based conflict analysis model and method over two universes[J]. Information Sciences, 2016, 372, 111- 125.
doi: 10.1016/j.ins.2016.08.030
15 LANG G , LUO J , YAO Y . Three-way conflict analysis: a unification of models based on rough sets and formal concept analysis[J]. Knowledge-Based Systems, 2020, 194, 105556.
doi: 10.1016/j.knosys.2020.105556
16 ATANASSOV K . Intuitionistic fuzzy sets[J]. International Journal Bioautomation, 2016, 20, 1- 6.
17 ATANASSOV K T . A second type of intuitionistic fuzzy sets[J]. Busefal, 1993, 56, 66- 70.
18 YAGER R R . Generalized orthopair fuzzy sets[J]. IEEE Transactions on Fuzzy Systems, 2016, 25 (5): 1222- 1230.
19 GARG H , CHEN S M . Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets[J]. Information Sciences, 2020, 517, 427- 447.
doi: 10.1016/j.ins.2019.11.035
20 XING Y , ZHANG R , ZHOU Z , et al. Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making[J]. Soft Computing, 2019, 23 (22): 11627- 11649.
doi: 10.1007/s00500-018-03712-7
21 LIU P , CHEN S M , WANG P . Multiple-attribute group decision-making based on q-rung orthopair fuzzy power maclaurin symmetric mean operators[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 50 (10): 3741- 3756.
22 LIU P , LIU W . Multiple-attribute group decision-making based on power Bonferroni operators of linguistic q-rung orthopair fuzzy numbers[J]. International Journal of Intelligent Systems, 2019, 34 (4): 652- 689.
doi: 10.1002/int.22071
23 LIU P , WANG P . Multiple-attribute decision-making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers[J]. IEEE Transactions on Fuzzy Systems, 2018, 27 (5): 834- 848.
24 LIU Z , WANG S , LIU P . Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators[J]. International Journal of Intelligent Systems, 2018, 33 (12): 2341- 2363.
doi: 10.1002/int.22032
25 WEI G , GAO H , WEI Y . Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making[J]. International Journal of Intelligent Systems, 2018, 33 (7): 1426- 1458.
doi: 10.1002/int.21985
26 XU L , LIU Y , LIU H . Some improved q-rung orthopair fuzzy aggregation operators and their applications to multiattribute group decision-making[J]. Mathematical Problems in Engineering, 2019, 2019, 1- 18.
27 YANG W , PANG Y . New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making[J]. International Journal of Intelligent Systems, 2019, 34 (3): 439- 476.
doi: 10.1002/int.22060
28 WANG P , WANG J , WEI G , et al. Similarity measures of q-rung orthopair fuzzy sets based on cosine function and their applications[J]. Mathematics, 2019, 7 (4): 340.
doi: 10.3390/math7040340
29 ZHANG Z , CHEN S M . Group decision making with incomplete q-rung orthopair fuzzy preference relations[J]. Information Sciences, 2021, 553, 376- 396.
doi: 10.1016/j.ins.2020.10.015
30 ALI M I . Another view on q-rung orthopair fuzzy sets[J]. International Journal of Intelligent Systems, 2018, 33 (11): 2139- 2153.
doi: 10.1002/int.22007
31 DU W S . Minkowski-type distance measures for generalized orthopair fuzzy sets[J]. International Journal of Intelligent Systems, 2018, 33 (4): 802- 817.
doi: 10.1002/int.21968
32 ALI Z , MAHMOOD T . Maclaurin symmetric mean operators and their applications in the environment of complex q-rung orthopair fuzzy sets[J]. Computational and Applied Mathematics, 2020, 39 (3): 1- 27.
33 PENG X , LIU L . Information measures for q-rung orthopair fuzzy sets[J]. International Journal of Intelligent Systems, 2019, 34 (8): 1795- 1834.
doi: 10.1002/int.22115
34 WEI G , WEI C , WANG J , et al. Some q-rung orthopair fuzzy maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization[J]. International Journal of Intelligent Systems, 2019, 34 (1): 50- 81.
35 KAMACI H, PETCHIMUTHU S. Some similarity measures for interval-valued bipolar q-rung orthopair fuzzy sets and their application to supplier evaluation and selection in supply chain management[J/OL]. Environment, Development and Sustainability, 2022. https://doi.org/10.1007/s10668-022-02130-y.
36 WANG C , HUANG Y , DING W , et al. Attribute reduction with fuzzy rough self-information measures[J]. Information Sciences, 2021, 549, 68- 86.
37 ZADEH L A . Fuzzy sets[J]. Information and Control, 1965, 8 (3): 338- 353.
38 DUBOIS D , PRADE H . Rough fuzzy sets and fuzzy rough sets[J]. International Journal of General System, 1990, 17 (2/3): 191- 209.
39 GRECO S, MATARAZZO B, SLOWINSKI R. Fuzzy similarity relation as a basis for rough approximations[C]//International Conference on Rough Sets and Current Trends in Computing. Berlin: Springer, 1998: 283-289.
40 DU J , LIU S , LIU Y , et al. A novel approach to three-way conflict analysis and resolution with Pythagorean fuzzy information[J]. Information Sciences, 2022, 584, 65- 88.
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