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中国管理科学

中国管理科学 >

2025 , Vol. 33 >Issue 4: 120 - 130

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

预算约束下考虑属性关联的最大效用共识模型

  • 程栋 ,
  • 侯剑琳 ,
  • 程发新
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  • 1.东华大学旭日工商管理学院，上海 200051
    2.江苏大学管理学院，江苏 镇江 212013
程栋（1989-），男（汉族），湖北黄冈人，东华大学旭日工商管理学院，副教授，博士，研究方向：群决策理论与应用、行为共识建模、环境管理等，E-mail: chengdong@dhu.edu.cn.

收稿日期: 2022-02-18

  修回日期: 2022-06-17

  网络出版日期: 2025-04-29

基金资助

国家自然科学基金项目(71901058);中央高校基本科研业务专项资金项目(2232018H-07)

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Maximum Utility Consensus Models with Interacting Attributes under Budget Constraints

  • Dong Cheng ,
  • Jianlin Hou ,
  • Faxin Cheng
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  • 1.Glorious Sun School of Business & Management，Donghua University，Shanghai 200051，China
    2.School of Management，Jiangsu University，Zhenjiang 212013，China

Received date: 2022-02-18

  Revised date: 2022-06-17

  Online published: 2025-04-29

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摘要

多属性群决策的关键问题之一是决策者如何对多属性意见达成共识，而多个属性之间的关联关系将影响决策者对各属性意见的调整以及最终共识结果。然而，现有研究大多假设各属性之间相互独立，忽视了属性之间关联关系对共识成本和决策者共识效用的影响。据此，本文探索多属性关联情形下如何利用有限预算获取最大效用的共识决策问题。首先，针对多个属性之间的关联关系，引入Choquet积分，构建基于属性关联的最小成本共识模型。其次，考虑决策者共识效用和共识成本预算约束，构建了具有预算约束的属性关联最大效用共识模型。为了确保模型具有最优解，又构建了交互关系优化模型以确定属性间交互权重的取值范围。最后，以政府与农户之间制定退耕还林合同为背景，验证了共识模型的有效性。结果表明：（1）同属性独立的群体共识决策模型相比，属性之间的冗余关系会提高共识成本，而属性间互补关系会降低共识成本。（2）属性间互补关系和冗余关系都会提高群体共识效用，且交互关系越强对共识效用的作用效果越显著。（3）属性间的冗余关系对共识成本与共识效用的影响比互补关系对二者影响更大。因此，在共识决策中应充分考虑属性之间的关联关系，兼顾合理的平衡成本预算与共识效用将有助于实现有限资源下的共识效用最大化。

关键词： 共识决策; 最大效用; 属性关联; 预算约束; Choquet积分

本文引用格式

程栋 , 侯剑琳 , 程发新 . 预算约束下考虑属性关联的最大效用共识模型[J]. 中国管理科学, 2025 , 33(4) : 120 -130 . DOI: 10.16381/j.cnki.issn1003-207x.2022.0297

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

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