Consensus-reaching method for social network large-scale group decision-making with linguistic distributed preference relations

doi:10.23919/JSEE.2026.000148

Abstract

Abstract:

Large-scale group decision-making (LSGDM), as a unique form of group decision-making, has been extensively studied. Its characteristic lies in the large number of decision-makers (DMs), resulting in a certain degree of complexity in the decision-making process. In the social network environment, DMs typically have some form of social relationship, influencing each other’s decision information. Considering the interactive connections among DMs, this paper proposes a model for LSGDM that takes into account community opinion leaders. Firstly, experts use linguistic distributed preference relations (LDPRs) to express assessment opinions. Different from the traditional approach that assigns the same semantic information to each expert, we construct a consistency-driven optimization model to obtain personalized individual semantics (PIS) of experts and language preferences are transformed into fuzzy numerical preferences. Secondly, combining social relationships and preference information among experts, the classic community detection algorithm is improved to partition large-scale groups into communities. Additionally, a feedback mechanism is designed to identify community opinion leaders and provide preference adjustment suggestions for experts. Finally, the feasibility and effectiveness of the proposed consensus decision-making model are verified through a specific case analysis.

Key words: large-scale group decision-making (LSGDM), consensus reaching process, social network, linguistic distributed preference, opinion leaders

Junfeng Chu, Yanyan Su, Pan Shu, Yanyan Wang, Yingming Wang. Consensus-reaching method for social network large-scale group decision-making with linguistic distributed preference relations[J]. Journal of Systems Engineering and Electronics, 2026, 37(5): 1642-1664.

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Symbol	Meaning of symbols
${\boldsymbol{A}} = {\left( {{a_{ij}}} \right)_{m \times m}}$	Adjacency matrix of the social network graph of decision experts
${\bf{TD}} = {\left[ {\left( {{t_{uv}},{d_{uv}}} \right)} \right]_{m \times m}}$	Trust relationship matrix among decision experts
${\boldsymbol{D}} = {\left( {{d_{ij}}} \right)_{n \times n}}$	LDPR of decision experts
${\boldsymbol{F}} = {\left( {{f_{ij}}} \right)_{n \times n}}$	FRR of decision experts
$ E = \left\{ {{e_1},{e_2},\cdots ,{e_m}} \right\}\left( {m \geqslant 20} \right) $	Set of decision experts
$X{\text{ = }}\left\{ {{x_1},{x_2},\cdots ,{x_n}} \right\}$	Set of alternative solutions
$\tilde {{{\boldsymbol{w}}_i}} = {\left( {{w_1},{w_2},\cdots ,{w_{{n_k}}}} \right)^\text{T}}$	Weight information of experts in community
$\tilde {\boldsymbol{\lambda}} = {\left( {{\lambda _1},{\lambda _2},\cdots ,{\lambda _t}} \right)^\text{T}}$	Weight information of each community
${w_{kl}}\left( {k,l = 1,2,\cdots ,m} \right)$	Weight information of edges between expert nodes ${e_k}$ and ${e_l}$

e	${\text{PNS}^k}\left( {{s_0}} \right)$	${\text{PNS}^k}\left( {{s_1}} \right)$	${\text{PNS}^k}\left( {{s_2}} \right)$	${\text{PNS}^k}\left( {{s_3}} \right)$	${\text{PNS}^k}\left( {{s_4}} \right)$	${\text{PNS}^k}\left( {{s_5}} \right)$	${\text{PNS}^k}\left( {{s_6}} \right)$
${e_1}$	0	0.2857	0.42	0.5	0.58	0.7143	1
${e_2}$	0	0.2857	0.42	0.5	0.58	0.7143	1
${e_3}$	0	0.2857	0.3810	0.5	0.6190	0.7143	1
${e_4}$	0	0.2857	0.42	0.5	0.58	0.7143	1
${e_5}$	0	0.2857	0.4200	0.5	0.58	0.7143	1
${e_6}$	0	0.2857	0.3657	0.5	0.6343	0.7143	1
${e_7}$	0	0.2857	0.42	0.5	0.58	0.7143	1
${e_8}$	0	0.1978	0.42	0.5	0.58	0.8022	1
${e_9}$	0	0.2857	0.42	0.5	0.58	0.7143	1
${e_{10}}$	0	0.22	0.42	0.5	0.58	0.78	1
${e_{11}}$	0	0.2857	0.3657	0.5	0.6343	0.7143	1
${e_{12}}$	0	0.2857	0.42	0.5	0.58	0.7143	1
${e_{13}}$	0	0.2857	0.42	0.5	0.8	0.7143	1
${e_{14}}$	0	0.1979	0.3377	0.5	0.6623	0.8021	1
${e_{15}}$	0	0.1429	0.42	0.5	0.58	0.8571	1
${e_{16}}$	0	0.1429	0.42	0.5	0.58	0.8571	1
${e_{17}}$	0	0.2857	0.4093	0.5	0.5906	0.7143	1
${e_{18}}$	0	0.2857	0.3657	0.5	0.6343	0.7143	1
${e_{19}}$	0	0.2857	0.3810	0.5	0.6190	0.7143	1
${e_{20}}$	0	0.2857	0.3657	0.5	0.6343	0.7143	1

Expert pair	Similarity	Expert pair	Similarity	Expert pair	Similarity	Expert pair	Similarity
${\text{sm}^{1,3}}$	0.9216	${\text{sm}^{11,14}}$	0.9327	${\text{sm}^{9,11}}$	0.9192	${\text{sm}^{11,17}}$	0.9411
${\text{sm}^{2,3}}$	0.9186	${\text{sm}^{6,7}}$	0.9208	${\text{sm}^{9,16}}$	0.8818	${\text{sm}^{12,14}}$	0.9286
${\text{sm}^{3,4}}$	0.8999	${\text{sm}^{6,8}}$	0.9540	${\text{sm}^{10,11}}$	0.9808	${\text{sm}^{13,14}}$	0.8974
${\text{sm}^{3,7}}$	0.8055	${\text{sm}^{6,9}}$	0.9047	${\text{sm}^{10,17}}$	0.9296	${\text{sm}^{14,15}}$	0.9647
${\text{sm}^{4,5}}$	0.9007	${\text{sm}^{6,10}}$	0.9751	${\text{sm}^{10,18}}$	0.9529	${\text{sm}^{14,16}}$	0.9713
${\text{sm}^{4,7}}$	0.8072	${\text{sm}^{6,16}}$	0.9575	${\text{sm}^{10,19}}$	0.9567	${\text{sm}^{17,19}}$	0.9461
${\text{sm}^{5,6}}$	0.9040	${\text{sm}^{7,8}}$	0.8874	${\text{sm}^{11,12}}$	0.9485	${\text{sm}^{17,20}}$	0.9160
${\text{sm}^{5,18}}$	0.9138	${\text{sm}^{9,10}}$	0.9135	${\text{sm}^{11,16}}$	0.9476

Community	Weight
${e_1}$	0.0596
${e_3}$	0.1282
${e_2}$	0.0594
${e_4}$	0.1075
${e_7}$	0.1360
${e_5}$	0.1179
${e_6}$	0.1935
${e_{18}}$	0.0988
${e_8}$	0.0990

Community	Weight
${e_9}$	0.1706
${e_{16}}$	0.1711
${e_{11}}$	0.2156
${e_{12}}$	0.1042
${e_{14}}$	0.1863
${e_{13}}$	0.0762
${e_{15}}$	0.0751