群体智慧下考虑模块化不信任关系的多属性大群体决策方法

doi:10.16381/j.cnki.issn1003-207x.2023.1302

Abstract

Abstract:

Due to the complex social connections between individuals， considering different decision-making behaviors has important theoretical value and practical significance in solving decision-making problems in large groups. However， most studies are based on different decision-making behaviors to enhance group consensus， and there is relatively little research on considering decision-making behaviors to enhance group intelligence at different levels of consensus， ultimately achieving the goal of improving the quality of group decision-making. Meanwhile， most studies focus on trust relationships， with less emphasis on modular thinking that treats clustering as a small group and considers situations where decision-makers have distrust relationships. To solve these problems， a new multi-attribute large group decision making method with interval intuitionistic is proposed fuzzy sets considering modular distrust relations. Firstly， based on the social network structure among decision experts， the Louvain method is used to divide the group decision-makers into subgroups and calculate the weights of the decision-makers and subgroups； Secondly， based on the density of social relationships and considering both trust and distrust relationships， the preference of decision experts is adjusted， and the level of group consensus is measured based on the similarity of individual and group preferences in position and direction； Then， fuzzy entropy and cross entropy are used to determine the attribute weight of the scheme， and the scoring function and accurate function of the scheme are calculated to determine the optimal scheme； Finally， taking the selection of emergency plans in major natural disaster events as the background， the effectiveness of the method are verified.This method considers the modular distrust relationship of decision-makers and selects the preference adjustment model of decision experts based on social relationship density to stimulate decision-makers to jointly explore better solutions. The example results demonstrate that the proposed consensus model can not only explore better decision-making solutions， but also effectively improve decision-making speed and meet the urgent needs of emergency decision-making.

Key words: large group decision-making, distrust relationship, louvain method, collective intelligence

CLC Number:

C934

Faming Zhang,Luping Lin,Zhaoqing Ye. A Multi-attribute Large Group Decision-making Method Considering Modular Distrust Relationships under Group Intelligence[J]. Chinese Journal of Management Science, 2026, 34(6): 215-227.

Figures/Tables 11

邻接矩阵

图论

代数式

A = 0110000100011000

$e 1 R e 2$ $e 1 R e 3$

$e 2 R e 4$ $e 3 R e 4$

$e 4 R e 1$

专家	方案	$f 1$	$f 2$	$f 3$
$e 1$	$x 1$	([0.90,0.91], [0.00,0.01])	([0.50,0.51], [0.40,0.41])	([0.70,0.71], [0.20,0.21])
	$x 2$	([0.25,0.26], [0.60,0.61])	([0.50,0.51], [0.40,0.41])	([0.70,0.71], [0.20,0.21])
	$x 3$	([0.50,0.51], [0.40,0.41])	([0.25,0.26], [0.60,0.61])	([0.70,0.71], [0.20,0.21])
$e 2$	$x 1$	([0.60,0.61], [0.30,0.31])	([0.70,0.71], [0.20,0.21])	([0.25,0.26], [0.60,0.61])
	$x 2$	([0.25,0.26], [0.60,0.61])	([0.70,0.71], [0.20,0.21])	([0.90,0.91], [0.00,0.01])
	$x 3$	([0.60,0.61], [0.30,0.31])	([0.25,0.26], [0.60,0.61])	([0.40,0.41], [0.50,0.51])
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
$e 19$	$x 1$	([0.70,0.71], [0.20,0.21])	([0.80,0.81], [0.10,0.11])	([0.80,0.81], [0.10,0.11])
	$x 2$	([0.10,0.11], [0.75,0.76])	([0.70,0.71], [0.20,0.21])	([0.25,0.26], [0.60,0.61])
	$x 3$	([0.10,0.11], [0.75,0.76])	([0.50,0.51], [0.40,0.41])	([0.70,0.71], [0.20,0.21])
$e 20$	$x 1$	([0.50,0.51], [0.40,0.41])	([0.60,0.61], [0.30,0.31])	([0.80,0.81], [0.10,0.11])
	$x 2$	([0.60,0.61], [0.30,0.31])	([0.25,0.26], [0.60,0.61])	([0.60,0.61], [0.30,0.31])
	$x 3$	([0.25,0.26], [0.60,0.61])	([0.50,0.51], [0.40,0.41])	([0.70,0.71], [0.20,0.21])

社区子群	决策专家	专家权重	子群权重
$C 1$	${e 1, e 2, e 9, e 14}$	$W 1 = (0.225,0.194,0.230,0.251) T$	0.112
$C 2$	${e 10, e 15, e 16, e 17, e 18, e 20}$	$W 3 = (0.129,0.272,0.226,0.131,0.097,0.145) T$	0.414
$C 3$	${e 4, e 8, e 11, e 13}$	$W 2 = (0.207,0.269,0.216,0.308) T$	0.127
$C 4$	${e 3, e 5, e 6, e 7, e 12, e 19}$	$W 4 = (0.153,0.167,0.206,0.150,0.155,0.169) T$	0.347

$D E N S (C 1)$	$D E N S (C 2)$	$D E N S (C 3)$	$D E N S (C 4)$
0.518	0.299	0.473	0.591

方案	$f 1$	$f 2$	$f 3$
$x 1$	([0.676,0.690 ], [0.000,0.141 ])	([0.529,0.540 ], [0.364,0.375 ])	([0.376,0.388 ], [0.482,0.494 ])
$x 2$	([0.477,0.487 ], [0.407,0.418 ])	([0.349,0.360 ], [0.521,0.532 ])	([0.615,0.632 ], [0.000,0.163 ])
$x 3$	([0.685,0.697 ], [0.194,0.206 ])	([0.417,0.427 ], [0.469, 0.479])	([0.348,0.359 ], [0.522,0.533 ])

方案	$f 1$	$f 2$	$f 3$
$x 1$	([0.621, 0.631], [0.275, 0.285])	([0.392, 0.403], [0.496, 0.507])	([0.379, 0.390], [0.493, 0.504])
$x 2$	([0.658, 0.668], [0.241, 0.251])	([0.335, 0.346], [0.544, 0.554])	([0.819, 0.830], [0.000, 0.052])
$x 3$	([0.312, 0.323], [0.563, 0.573])	([0.759, 0.769], [0.137, 0.148])	([0.700, 0.710], [0.200, 0.210])

方案	$f 1$	$f 2$	$f 3$
$x 1$	([0.754, 0.766], [0.000, 0.101])	([0.599, 0.613], [0.000, 0.230])	([0.596, 0.610], [0.000, 0.236])
$x 2$	([0.670, 0.683], [0.000, 0.154])	([0.573, 0.587], [0.000, 0.259])	([0.609, 0.621], [0.000, 0.256])
$x 3$	([0.522, 0.533], [0.365, 0.377])	([0.491, 0.501], [0.393, 0.404])	([0.508, 0.519], [0.377, 0.388])

模型	考虑因素	调整次数	共识度	各方案得分函数	排序
$A$	信任-不信任	4	0.8502	$(0.588,0.522,0.129)$	$x 1 ≻ x 2 ≻ x 3$
$B$	信任关系	10	0.8573	$(0.474,0.626,0.182)$	$x 2 ≻ x 1 ≻ x 3$
$C$	信任-相似	2	0.8650	$(0.501,0.552,0.178)$	$x 2 ≻ x 1 ≻ x 3$

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A Multi-attribute Large Group Decision-making Method Considering Modular Distrust Relationships under Group Intelligence

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