预算约束下考虑属性关联的最大效用共识模型

doi:10.16381/j.cnki.issn1003-207x.2022.0297

Abstract

Abstract:

One of the key problems in multi-attribute group decision-making （MAGDM） is how to reach a consensus on multi-attribute opinions， while the interaction between attributes will affect the adjustment of decision-makers' opinions on each attribute and the consensus outcome. However， the extant research often assumes that attributes are independent of each other and ignores the impact of their interactions on consensus efficiency and decision-maker's consensusutility. It aims to explore the consensus problem of how to obtain the maximumconsensus utility with a limited budget considering interacting attributes. First， Choquet integral is introduced to solve the interacting relationship among multiple attributes， and a minimum cost consensus model with interacting attributes is built. Second， considering thedecision-maker's consensus utility and limited budget， a maximum utility consensus model with interacting attributesunder budget constraints is constructed. To ensure that the proposed model has the optimal solution， an interaction optimization model is built to determine the range of the interaction weight between attributes. Finally， the consensus model is validated by thecontract negotiation between the government and farmers. Results show that：（1） Compared with independent attributes， the negative interaction between attributes can increase the consensus cost， while the positive one reduces the consensus cost；（2） Both attribute complementary and redundant relationship will improve the group consensus utility， and the stronger the interaction relationship， the more significant the effect on consensus utility；（3） The redundant relationship between attributes has a greater impact on consensus cost and consensus utility than the complementary relationship. Thus， the interaction of attributes should be fully considered in consensus decision-making， and a reasonable balance between the cost budget and consensus utility will help to maximize consensus utility.It can also provide theoretical reference and methodology support forMAGDMwithinteracting attributes in this study.

Key words: consensus decision-making, maximum utility, interacting attributes, budget constraints, Choquet integral

CLC Number:

C934

Dong Cheng,Jianlin Hou,Faxin Cheng. Maximum Utility Consensus Models with Interacting Attributes under Budget Constraints[J]. Chinese Journal of Management Science, 2025, 33(4): 120-130.

Figures/Tables 9

符号	含义
$l j$	属性 $v j$ 上意见值的跨度
$Δ o i j$	$d i$ 在属性 $v j$ 上的意见偏差
$e i j$	$d i$ 在 $v j$ 上调整意见的百分比平方
$I i j$	$d i$ 在属性 $v j$ 上的Shapley值
$μ i (S j)$	集合 $S j$ 的模糊测度
$a (S)$	集合 $S$ 中属性间的交互权重
$p i$	决策者 $d i$ 的总成本
$η$	成本预算值
$x i j k, t i j k, α i j k, β i j k$	中间变量
$y j$	属性 $v j$ 的类型指示变量
$u i j$	$d i$ 在属性 $v j$ 上的效用值
$u (i j)$	排序后 $d i$ 在属性 $v j$ 上效用值
$u i$	$d i$ 的总效用值

属性集 $S$	$a (S)$
{ $v 1, v 2$ }	0.11
{ $v 1, v 3$ }	-0.1
{ $v 2, v 3$ }	0.4

交互权重 ${a (v 1, v 2), a (v 1, v 3), a (v 2, v 3)}$	总成本	总共识效用
${0,0, 0}$	76.873	0.832
${0, - 0.1,0}$	87.841	0.845
${0, - 0.2,0}$	98.670	0.863
${0, - 0.3,0}$	109.440	0.886
${0, - 0.4,0}$	120.163	0.911
${0, - 0.5,0}$	130.823	0.927
${0.1, - 0.1,0.1}$	76.232	0.835
${0.2, - 0.1,0.1}$	75.748	0.840
${0.3, - 0.1,0.1}$	74.791	0.845
${0.4, - 0.1,0.1}$	74.600	0.850
${0.1, - 0.1,0.2}$	64.989	0.827
${0.2, - 0.1,0.2}$	64.507	0.834
${0.3, - 0.1,0.2}$	63.958	0.840
${0.1, - 0.1,0.3}$	53.694	0.831
${0.2, - 0.1,0.3}$	53.210	0.839
${0.1, - 0.2,0.1}$	87.053	0.847
${0.2, - 0.2,0.1}$	86.579	0.852
${0.3, - 0.2,0.1}$	86.051	0.856
${0.1, - 0.3,0.1}$	97.806	0.865
${0.2, - 0.3,0.1}$	97.291	0.869

References 37

1	缑迅杰，邓富民，徐泽水.基于自信双层语言偏好关系的大规模群体共识决策方法及其应用研究［J］. 中国管理科学，2023，31（9）：222-232.
	Gou X J， Deng F M， Xu Z S. The application of the large-scale group consensus decision-making method based on self-confident double hierarchy linguistic preference relations［J］. Chinese Journal of Management Science， 2023， 31（9）： 222-232.
2	姚升保，古淼.移情关系影响下的群体共识决策模型研究［J］. 中国管理科学， 2021， 29（11）： 203-214.
	Yao S B， Gu M. A consensus model for group decision making under the influence of empathy［J］. Chinese Journal of Management Science， 2021， 29（11）： 203-214.
3	张恒杰，朱文凤，董玉成.异质环境下基于最小冒犯准则的分类共识决策方法研究［J］. 系统工程理论与实践， 2022， 42（5）：1378-1390.
	Zhang H J， Zhu W F， Dong Y C. The classification-based consensus model with minimum violations in heterogeneous group decision making［J］. Systems Engineering-Theory & Practice， 2022， 42（5）： 1378-1390.
4	Jing F Y， Chao X R. Fairness concern： An equilibrium mechanism for consensus-reaching game in group decision-making［J］. Information Fusion， 2021， 72： 147-160.
5	Du J L， Liu S F， Liu Y. A limited cost consensus approach with fairness concern and its application［J］. European Journal of Operational Research， 2021，289（1）：261-275.
6	Ben-Arieh D， Easton T. Multi-criteria group consensus under linear cost opinion elasticity［J］. Decision support systems， 2007， 43（3）： 713-721.
7	Ben-Arieh D， Easton T， Evans B. Minimum cost consensus with quadratic cost functions［J］. IEEE Transactions on Systems， Man， and Cybernetics-Part A： Systems and Humans， 2008， 39（1）： 210-217.
8	Zhang G Q， Dong Y C， Xu Y F， et al. Minimum-cost consensus models under aggregation operators［J］. IEEE Transactions on Systems， Man， and Cybernetics-Part A： Systems and Humans， 2011， 41（6）： 1253-1261.
9	Zhang H H， Kou G， Peng Y. Soft consensus cost models for group decision making and economic interpretations［J］. European Journal of Operational Research， 2019， 277（3）： 964-980.
10	程栋，张静阳，袁宇翔，程发新.基于区间意见的非对称最小成本共识决策问题研究［J］.运筹与管理，2022，31（5）：43-48.
	Cheng D， Zhang J Y， Yuan Y X， Cheng F X. Research on minimum asymmetric cost consensus problem based on interval opinions［J］. Operations Research and Management Science， 2022， 31（5）： 43-48.
11	Gong Z W， Xu X X， Guo W W， et al. Minimum cost consensus modelling under various linear uncertain-constrained scenarios［J］. Information Fusion， 2021， 66： 1-17.
12	Cheng D， Zhou Z L， Cheng F X， et al. Modeling the minimum cost consensus problem in an asymmetric costs context［J］. European Journal of Operational Research， 2018， 270（3）： 1122-1137.
13	徐泽水，任珮嘉.犹豫模糊偏好决策研究进展与前景［J］.系统工程理论与实践， 2020， 40（8）： 2193-2202.
	Xu Z S， Ren P J. A survey of decision making with hesitant fuzzy preference relations： Progress and prospect［J］. Systems Engineering-Theory & Practice， 2020， 40（8）： 2193-2202.
14	Wu T， Liu X W， Gong Z W， et al. The minimum cost consensus model considering the implicit trust of opinions similarities in social network group decision-making［J］. International Journal of Intelligent Systems， 2020， 35（3）： 470-493.
15	Liu Y， Zhou T， Forrest J Y L. （2020）. A multivariate minimum cost consensus model for negotiations of holdout demolition［J］. Group Decision and Negotiation， 29（5）： 871-899.
16	Gong Z W， Xu X X， Lu F L， et al. On consensus models with utility preferences and limited budget［J］. Applied Soft Computing， 2015， 35： 840-849.
17	Cheng D， Yuan Y X， Wu Y， et al. Maximum satisfaction consensus with budget constraints considering individual tolerance and compromise limit behaviors［J］. European Journal of Operational Research， 2022， 297（1）： 221-238.
18	Guo W W， Gong Z W， Xu X X， et al. Linear uncertain extensions of the minimum cost consensus model based on uncertain distance and consensus utility［J］. Information Fusion， 2021， 70： 12-26.
19	Gong Z W， Xu C， Chiclana F， et al. Consensus measure with multi-stage fluctuation utility based on China’s urban demolition negotiation［J］. Group Decision and Negotiation， 2017， 26（2）： 379-407.
20	Gitinavard H， Shirazi M A， Zarandi M H F. Sustainable feedstocks selection and renewable products allocation： A new hybrid adaptive utility-based consensus model［J］. Journal of Environmental Management， 2020， 264： 110428.
21	Gong Z W， Xu X X， Li L S， et al. Consensus modeling with nonlinear utility and cost constraints： A case study［J］. Knowledge-Based Systems， 2015， 88： 210-222.
22	Zhong X Y， Xu X H， Pan B. A non-threshold consensus model based on the minimum cost and maximum consensus-increasing for multi-attribute large group decision-making［J］. Information Fusion， 2022， 77： 90-106.
23	Zhang B W， Dong Y C， Xu Y F. Multiple attribute consensus rules with minimum adjustments to support consensus reaching［J］. Knowledge-Based Systems， 2014， 67： 35-48.
24	Chen X， Xu W J， Liang H M， et al. The classification-based consensus in multi-attribute group decision-making［J］. Journal of the Operational Research Society， 2020， 71（9）： 1375-1389.
25	Yan H B， Ma T J， Huynh V N. On qualitative multi-attribute group decision making and its consensus measure： A probability based perspectivet［J］. Omega， 2017， 70： 94-117.
26	Li Y H， Kou G， Li G X， et al. Multi-attribute group decision making with opinion dynamics based on social trust network［J］. Information Fusion， 2021， 75： 102-115.
27	索玮岚，冯博. 关联型决策分析方法研究综述［J］. 系统工程理论与实践， 2016， 36（10）： 2449-2464.
	Suo W L， Feng B. Review on interdependent-decision analysis methods［J］. Systems Engineering-Theory & Practice， 2016， 36（10）： 2449-2464.
28	Carlsson C， Fullér R. Multiple criteria decision making： The case for interdependence［J］. Computers & Operations Research， 1995， 22（3）： 251-260.
29	Zhang L， Zhou D Q， Wang Y P， et al. An axiomatic approach of the ordered Sugeno integrals as a tool to aggregate interacting attributes［C］//2007 IEEE International Conference on Grey Systems and Intelligent Services.NanJing，November 18-20，2007： 231-234.
30	Mayag B， Bouyssou D. Necessary and possible interaction between criteria in a 2-additive Choquet integral model［J］. European Journal of Operational Research， 2020， 283（1）： 308-320.
31	陈晓红，李慧，谭春桥. 考虑不同心理行为偏好的混合随机多属性决策［J］. 系统工程理论与实践， 2018， 38（6）： 1545-1556.
	Chen X H， Li H， Tan C Q. A hybrid stochastic multi-attribute decision-making method considering different psychological behavior［J］. Systems Engineering-Theory & Practice， 2018， 38（6）： 1545-1556.
32	Gong Z W， Guo W W， Slowiński R. Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction［J］. Omega， 2021， 104： 102491.
33	Marichal J L， Roubens M. Determination of weights of interacting criteria from a reference set［J］. European Journal of Operational Research， 2000， 124（3）： 641-650.
34	Tehrani A F. The choquet kernel on the use of regression problem［J］. Information Sciences， 2021， 556： 256-272.
35	Marichal J L. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria［J］. IEEE Transactions on Fuzzy Systems， 2000， 8（6）： 800-807.
36	Li H H， Ji Y， Qu S J. Two-stage stochastic integrated adjustment deviations and consensus models in an asymmetric costs context［J］. Journal of Intelligent & Fuzzy Systems， 2021， 40（6）： 12301-12319 .
37	Tan X， Gong Z W， Chiclana F， et al. Consensus modeling with cost chance constraint under uncertainty opinions［J］. Applied Soft Computing， 2018， 67： 721-727.

文献	单属性还是多属性？	是否考虑属性关联？	是否考虑成本预算？	是否考虑个体共识效用？	共识模型类型
[13]	单属性	否	是	是	最大效用共识模型
[32]	单属性	否	否	否	最小成本共识模型
[37]	单属性	否	是	是	最小成本共识模型
[3]	多属性	否	否	否	最小成本共识模型
[10]	多属性	是	否	否	最小成本共识模型
[18]	多属性	否	否	否	最小调整共识模型
本文	多属性	是	是	是	最大效用共识模型

[1]	Yu Feng, Yaoguo Dang, Junjie Wang, Zhangcheng Yang. Grey Incidence Decision-making Method with Mixed Information Based on 2-additive Choquet Integral and Its Application [J]. Chinese Journal of Management Science, 2025, 33(9): 189-200.
[2]	LUO Shi-hua, LIU Jun. A Novel Sort Method for Trapezoidal Intuitionistic Fuzzy MAGDM with Choquet Bonferroni Means [J]. Chinese Journal of Management Science, 2020, 28(1): 134-143.
[3]	WANG Da-ao, JIAN Li-rong, WANG Hui, LIU Si-feng. Study on Profit Allocation of Industrial Cluster Based on Restricted Cooperative Game [J]. Chinese Journal of Management Science, 2019, 27(4): 171-178.
[4]	YANG Na, LIAO Xiu-wu, LEI Hong-zhen. Two Stage Winner Determination Approach with Interacting Attributes [J]. Chinese Journal of Management Science, 2019, 27(10): 148-158.
[5]	ZHAO Shu-ping, LIANG Chang-yong, LUO Da-wei. Multi-Attribute Group Decision Making Based On Extend VIKOR and Induced Generalized Intuitionistic Trapezoidal Fuzzy Choquet Integral [J]. Chinese Journal of Management Science, 2016, 24(6): 132-142.
[6]	WAN Shu-ping, DONG Jiu-ying. Multi-attribute Decision Making based on Triangular Intuitionistic Fuzzy Number Choquet Integral Operator [J]. Chinese Journal of Management Science, 2014, 22(3): 121-129.
[7]	CHENG Bin-hong. Soft Budget Constraints and Transformation of the State-Owned Enterprise：Factor Input Analysis [J]. Chinese Journal of Management Science, 2007, 15(2): 15-20.
[8]	WANG Yan, LI Chu-lin. Asymmetric Multiple-Object Auctions [J]. Chinese Journal of Management Science, 2003, (6): 61-65.

Maximum Utility Consensus Models with Interacting Attributes under Budget Constraints

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 9

References 37

Related Articles 8

Metrics

Comments

Recommended 0