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

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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

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Maximum Utility Consensus Models with Interacting Attributes under Budget Constraints

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