JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 77-90.doi: 10.6040/j.issn.1671-9352.4.2022.9449

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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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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

CLC Number: 

  • TP18

Fig.1

q-rung orthopair fuzzy set"

Table 1

q-ROFIS of Mideast conflict"

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)

Table 2

Three alliances of agents and issues"

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}

Table 3

Feasible strategies of Mideast conflict"

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}

Table 4

Self-information of feasible strategies of Mideast conflict"

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

Table 5

The change of optimal feasible strategy related to c°"

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}

Table 6

The change of optimal feasible strategy related to c°"

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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