基于偏好—赞成结构与前景理论的双边匹配决策方法

doi:10.16381/j.cnki.issn1003-207x.2023.1936

摘要/Abstract

摘要：

针对偏好-赞成结构下的双边匹配问题，考虑到不同决策者对属性权重的不同观点以及有限理性的心理行为，提出一种基于偏好-赞成结构与前景理论的双边匹配决策方法。首先，考虑到多决策者的属性权重分歧情况，构建一种新的考虑属性权重的优化模型，提出一种双边主体多属性偏好-赞成结构信息聚合方法，能够有效解决属性非等权重的多属性信息聚合问题。其次，根据偏好-赞成结构信息特点，通过赞成数量关系，提出双边主体个体参考点与社会参考点的确定方法，构建基于前景理论的双边主体综合感知价值函数模型。在此基础上，设计效用最大化目标的双边匹配优化方法，充分体现决策者有限理性。最后，通过某养老机构老年人与护工匹配的案例说明提出方法的可行性和有效性。

关键词: 双边匹配, 偏好-赞成结构, 聚合模型, 前景理论, 养老机构

Abstract:

China has become an aging society and the pension issue has become a focus of national concern. With the increase of the number of elderly people， traditional family support mode has encountered many problems， such as family size shrinking and birth rate declining. Institutional pension is the key to solve the above problems. However， the nursing resources in nursing institutions are in short supply， especially in public institutions. Therefore， it is necessary to improve the utilization rate of nursing resources by the effective matching of elderly people and caregivers. To address this issue， a two-sided matching decision-making method is proposed based on preference-approval structure and prospect theory considering different opinions of different decision makers on attribute weights and the psychological behavior of bounded rationality. Firstly， a fusion model for aggregating preference-approval structures information from two-sided decision makers for attributes is proposed. Then， prospect theory is used to construct a comprehensive perceived utility model of the two-sided agents based on the new method of constructing individual reference points and social reference points of both agents. And a two-sided matching method with the objective of utility maximization is constructed. Finally， a case of matching elder people with caregivers in an elderly care institution is used to illustrate the effectiveness and feasibility of the proposed method. It can be seen through case analysis that our proposed method can effectively solve the problem of the effective matching of elderly people and caregivers.

Key words: two-sided matching, preference-approval structure, fusion model, prospect theory, elderly care institution

中图分类号:

C934

李鹏,王可,徐志伟. 基于偏好—赞成结构与前景理论的双边匹配决策方法[J]. 中国管理科学, 2026, 34(3): 181-191.

Peng Li,Ke Wang,Zhiwei Xu. A Two-sided Matching Decision-making Method Based on Preference-approval Structure and Prospect Theory[J]. Chinese Journal of Management Science, 2026, 34(3): 181-191.

图/表 8

图1

表 1

甲方主体Ei对乙方主体的PAS信息Hi=hqjis×n"

甲方主体		$B 1$	$B 2$	$B 3$	$B 4$	$B 5$	$B 6$	$B 7$
$E 1$	$e 1$	$2, 1$	$3, 1$	$5, 0$	$1, 1$	$7, 0$	$6, 0$	$4, 0$
	$e 2$	$6, 0$	$1, 1$	$7, 0$	$5, 0$	$4, 0$	$2, 1$	$3, 1$
	$e 3$	$5, 0$	$6, 0$	$3, 1$	$4, 0$	$2, 1$	$1, 1$	$7, 0$
$E 2$	$e 1$	$4, 0$	$2, 1$	$5, 0$	$1, 1$	$6, 0$	$3, 0$	$7, 0$
	$e 2$	$2, 1$	$4, 1$	$6, 0$	$5, 0$	$3, 1$	$7, 0$	$1, 1$
	$e 3$	$3, 1$	$6, 0$	$4, 0$	$5, 0$	$7, 0$	$1, 1$	$2, 1$
$E 3$	$e 1$	$4, 0$	$2, 1$	$7, 0$	$5, 0$	$3, 0$	$6, 0$	$1, 1$
	$e 2$	$4, 0$	$6, 0$	$3, 0$	$1, 1$	$7, 0$	$2, 1$	$5, 0$
	$e 3$	$3, 1$	$4, 1$	$5, 0$	$2, 1$	$6, 0$	$1, 1$	$7, 0$
$E 4$	$e 1$	$2, 1$	$3, 1$	$1, 1$	$7, 0$	$6, 0$	$4, 1$	$5, 0$
	$e 2$	$5, 0$	$6, 0$	$3, 1$	$4, 1$	$2, 1$	$1, 1$	$7, 0$
	$e 3$	$3, 1$	$6, 0$	$5, 0$	$4, 0$	$7, 0$	$1, 1$	$2, 1$
$E 5$	$e 1$	$4, 0$	$2, 1$	$5, 0$	$1, 1$	$7, 0$	$6, 0$	$3, 1$
	$e 2$	$7, 0$	$1, 1$	$4, 0$	$3, 1$	$5, 0$	$2, 1$	$6, 0$
	$e 3$	$3, 1$	$4, 0$	$2, 1$	$6, 0$	$5, 0$	$7, 0$	$1, 1$

表 1

表 2

乙方主体Bj对甲方主体的PAS信息Gj=glijt×m"

乙方主体		$E 1$	$E 2$	$E 3$	$E 4$	$E 5$
$B 1$	$b 1$	$2, 1$	$3, 0$	$1, 1$	$5, 0$	$4, 0$
	$b 2$	$3, 1$	$2, 1$	$1, 1$	$5, 0$	$4, 0$
	$b 3$	$4, 0$	$1, 1$	$2, 1$	$5, 0$	$3, 0$
$B 2$	$b 1$	$3, 1$	$4, 0$	$2, 1$	$1, 1$	$5, 0$
	$b 2$	$3, 1$	$4, 0$	$1, 1$	$2, 1$	$5, 0$
	$b 3$	$5, 0$	$2, 1$	$1, 1$	$4, 0$	$3, 0$
$B 3$	$b 1$	$5, 0$	$1, 1$	$3, 1$	$4, 0$	$2, 1$
	$b 2$	$4, 0$	$2, 1$	$3, 0$	$5, 0$	$1, 1$
	$b 3$	$3, 0$	$4, 0$	$5, 0$	$1, 1$	$2, 1$
$B 4$	$b 1$	$3, 0$	$5, 0$	$2, 1$	$4, 0$	$1, 1$
	$b 2$	$2, 0$	$4, 0$	$5, 0$	$1, 1$	$3, 0$
	$b 3$	$1, 1$	$3, 0$	$4, 0$	$2, 1$	$5, 0$
$B 5$	$b 1$	$4, 0$	$1, 1$	$5, 0$	$3, 1$	$2, 1$
	$b 2$	$2, 1$	$3, 0$	$4, 0$	$5, 0$	$1, 1$
	$b 3$	$4, 0$	$1, 1$	$5, 0$	$3, 0$	$2, 1$
	$b 1$	$1, 1$	$2, 1$	$4, 0$	$5, 0$	$3, 1$
$B 6$	$b 2$	$5, 0$	$3, 0$	$2, 1$	$1, 1$	$4, 0$
	$b 3$	$2, 1$	$1, 1$	$3, 0$	$5, 0$	$4, 0$
	$b 1$	$2, 1$	$3, 0$	$1, 1$	$4, 0$	$5, 0$
$B 7$	$b 2$	$3, 0$	$1, 1$	$2, 1$	$4, 0$	$5, 0$
	$b 3$	$3, 0$	$2, 1$	$1, 1$	$5, 0$	$4, 0$

表 2

表3

甲方主体Ei对乙方主体的综合PAS评价矩阵H=hijm×n"

甲方主体	$B 1$	$B 2$	$B 3$	$B 4$	$B 5$	$B 6$	$B 7$
$E 1$	$2, 1$	$3, 0$	$7, 0$	$5, 0$	$5, 0$	$1, 1$	$5, 0$
$E 2$	$2, 1$	$4, 0$	$5, 0$	$1, 1$	$6, 0$	$3, 0$	$7, 0$
$E 3$	$3, 1$	$4.5, 0$	$6.5, 0$	$1, 1$	$6.5, 0$	$2, 1$	$4.5, 0$
$E 4$	$3, 1$	$6, 0$	$5, 0$	$4, 0$	$7, 0$	$1, 1$	$2, 1$
$E 5$	$3, 1$	$4, 0$	$5, 0$	$2, 1$	$6, 0$	$7, 0$	$1, 1$

表3

表4

乙方主体Bj对甲方主体的综合PAS评价矩阵G=gijm×n"

甲方主体	$B 1$	$B 2$	$B 3$	$B 4$	$B 5$	$B 6$	$B 7$
$E 1$	$3, 1$	$3, 1$	$4, 0$	$1, 1$	$4, 0$	$2, 1$	$3, 0$
$E 2$	$2, 1$	$4, 0$	$2, 1$	$4, 0$	$1, 1$	$1, 1$	$2, 0$
$E 3$	$1, 1$	$1, 1$	$3, 0$	$4, 0$	$5, 0$	$3, 0$	$1, 1$
$E 4$	$5, 0$	$2, 1$	$5, 0$	$2, 1$	$3, 0$	$5, 0$	$4, 0$
$E 5$	$4, 0$	$5, 0$	$1, 1$	$4, 0$	$2, 1$	$4, 0$	$5, 0$

表4

表 5

两方主体的个体参考点与社会参考点"

甲方主体	$c E i$	$f E i$	乙方主体	$c B j$	$f B j$
$E 1$	2.5	2.75	$B 1$ $B 2$ $B 3$ $B 4$ $B 5$ $B 6$ $B 7$	3.5	2
$E 2$	2.5	2.75	$B 2$ $B 2$ $B 3$ $B 4$ $B 5$ $B 6$ $B 7$	3.5	2
$E 3$	3.5	2.5	$B 3$	2.5	2.2
$E 4$	3.5	2.5	$B 4$	2.5	2.2
$E 5$	3.5	2.5	$B 5$	2.5	2.2
-	-	-	$B 6$	2.5	2.2
-	-	-	$B 7$	1.5	2.3

表 5

图2

表6

决策结果比较"

方法	匹配	未匹配
文献[32]方法	$E 1, B 4, E 2, B 1, E 3, B 7$ , $E 4, B 6, E 5, B 3$	$B 2, B 5$
本文所提方法	$E 1, B 6, E 2, B 1, E 3, B 2,$ $E 4, B 4, E 5, B 3$	$B 5, B 7$

表6

参考文献 32

[1]	Boudreau J W， Knoblauch V. A marriage matching mechanism menagerie［J］. Operations Research Letters， 2017， 45（1）： 68-71.
[2]	Yu D， Xu Z. Intuitionistic fuzzy two-sided matching model and its application to personnel-position matching problems［J］. Journal of the Operational Research Society， 2020， 71（2）： 312-321.
[3]	Yang Q， You X， Zhang Y. Two-sided matching based on I-BTM and LSGDM applied to high-level overseas talent and job fit problems［J］. Scientific Reports， 2021， 11： 12723.
[4]	Korkmaz İ， Gökçen H， Çetinyokuş T. An analytic hierarchy process and two-sided matching based decision support system for military personnel assignment［J］. Information Sciences， 2008， 178（14）： 2915-2927.
[5]	Li B， Yang Y， Su J， et al. Two-sided matching model for complex product manufacturing tasks based on dual hesitant fuzzy preference information［J］. Knowledge-Based Systems， 2019， 186： 104989.
[6]	Li B， Yang Y， Su J， et al. Two-sided matching decision-making model with hesitant fuzzy preference information for configuring cloud manufacturing tasks and resources［J］. Journal of Intelligent Manufacturing， 2020， 31（8）： 2033-2047.
[7]	Yang Q， Liu J， Liu X， et al. A two-sided matching model for task distribution in ridesharing： A sustainable operations perspective［J］. Sustainability， 2019， 11（7）： 2187.
[8]	Chen L T， Chen S Q. Volunteer multi-person multi-task optimization dispatch method considering two-sided matching［J］. Soft Computing， 2022， 26（8）： 3837-3861.
[9]	Chen S Q， Zhang L， Shi H L， et al. Two-sided matching model for assigning volunteer teams to relief tasks in the absence of sufficient information［J］. Knowledge-Based Systems， 2021， 232： 107495.
[10]	Haas C， Hall M. Two-Sided Matching for mentor-mentee allocations-Algorithms and manipulation strategies［J］. PLoS One， 2019， 14（3）： e0213323.
[11]	Gale D， Shapley L S. College admissions and the stability of marriage［J］. The American Mathematical Monthly， 1962， 69（1）： 9-15.
[12]	Roth A E. Common and conflicting interests in two-sided matching markets［J］. European Economic Review， 1985， 27（1）： 75-96.
[13]	Tan J J M. A necessary and sufficient condition for the existence of a complete stable matching［J］. Journal of Algorithms， 1991， 12（1）： 154-178.
[14]	Irving R W， Manlove D F， Scott S. The stable marriage problem with master preference lists［J］. Discrete Applied Mathematics， 2008， 156（15）： 2959-2977.
[15]	陈希，樊治平. 考虑多种形式信息的求职者与岗位双边匹配研究［J］.运筹与管理， 2009，18（6）： 103-109.
	Chen X， Fan Z P. Research on two-sided matching problem between employees and positions based on multiple format information［J］. Operations Research and Management Science， 2009， 18（6）： 103-109.
[16]	姜艳萍，孔德财，袁铎宁. 具有序区间偏好信息的双边稳定匹配决策方法［J］. 系统工程理论与实践， 2017， 37（8）： 2152-2161.
	Jiang Y P， Kong D C， Yuan D N. Two-sided stable matching decision-making method with ordinal interval preference［J］. Systems Engineering-Theory & Practice， 2017， 37（8）： 2152-2161.
[17]	乐琦，樊治平. 具有不确定偏好序信息的双边匹配决策问题研究［J］. 运筹与管理， 2012， 21（1）： 57-63.
	Yue Q， Fan Z P. Study on two-sided matching decision-making problems with uncertain preference ordinal information［J］. Operations Research and Management Science， 2012， 21（1）： 57-63.
[18]	Brams S J， Sanver M R. Voting systems that combine approval and preference［M］//Brams S J， Gehrlein W V， Roberts F S.The Mathematics of Preference， Choice and Order.Berlin，Heidelberg： Springer， 2009： 215-237.
[19]	Liang H， Xiong W， Dong Y. A prospect theory-based method for fusing the individual preference-approval structures in group decision making［J］. Computers and Industrial Engineering， 2018， 117（C）： 237-248.
[20]	Dong Y， Li Y， He Y， et al. Preference-approval structures in group decision making： Axiomatic distance and aggregation［J］. Decision Analysis， 2021， 18（4）： 273-295.
[21]	Liu H， Xu Z， Jiang L， et al. Multi-criteria group decision making with preference approval structures： A personalized individual semantics approach［J］. Information Fusion， 2023， 96： 80-91.
[22]	Jia X， Wang X， Zhu Y， et al. A two-sided matching decision-making approach based on regret theory under intuitionistic fuzzy environment［J］. Journal of Intelligent & Fuzzy Systems， 2021， 40（6）： 11491-11508.
[23]	Li P， Wang N， Wei C， et al. A two-sided matching method considering the lowest value of acceptability with regret theory for probabilistic linguistic term sets［J］. International Journal of Machine Learning and Cybernetics， 2021， 12（4）： 917-930.
[24]	汪凌，孙佳岐，高心仪. 考虑主体心理行为的毕达哥拉斯模糊多指标双边匹配决策方法［J］. 模糊系统与数学， 2022， 36（4）： 100-111.
	Wang L， Sun J Q， Gao X Y. Two-sided matching decision method with Pythagorean fuzzy and multi criteria considering agents’ phychological behavior［J］. Fuzzy Systems and Mathematics，2022，36（4）： 100-111.
[25]	Tversky A， Kahneman D. Advances in prospect theory： Cumulative representation of uncertainty［J］.Journal of Risk &Uncertainty， 1992， 5： 297-323.
[26]	Echenique F. What matchings can be stable？ The testable implications of matching theory［J］. Mathematics of Operations Research， 2008， 33（3）： 757-768.
[27]	Erdamar B， García-Lapresta J L， Pérez-Román D， et al. Measuring consensus in a preference-approval context［J］. Information Fusion， 2014， 17： 14-21.
[28]	Tian X， Ma J， Li L， et al. Development of prospect theory in decision making with different types of fuzzy sets： A state-of-the-art literature review［J］. Information Sciences， 2022， 615： 504-528.
[29]	Armstrong R D， Cook W D， Seiford L M. Priority ranking and consensus formation： The case of ties［J］. Management Science， 1982， 28（6）： 638-645.
[30]	罗骁，李为民，王璇子. 基于双参照点的双边匹配决策方法［J］. 控制与决策， 2019， 34（6）： 1286-1292.
	Luo X， Li W M， Wang X Z. Decision method for two-sided matching based on double reference points［J］. Control and Decision， 2019， 34（6）： 1286-1292.
[31]	Schwerter F. Social reference points and risk taking［J］. Management Science， 2024， 70（1）： 616-632.
[32]	乐琦，樊治平. 基于不完全序值信息的双边匹配决策方法［J］. 管理科学学报， 2015， 18（2）： 23-35.
	Yue Q， Fan Z P. Decision method for two-sided matching based on incomplete ordinal number information［J］. Journal of Management Sciences in China， 2015， 18（2）： 23-35.