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

Abstract

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

CLC Number:

C934

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.

Figures/Tables 8

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

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

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

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

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

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	$E 1, B 6, E 2, B 1, E 3, B 2,$ $E 4, B 4, E 5, B 3$	$B 5, B 7$

References 32

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A Two-sided Matching Decision-making Method Based on Preference-approval Structure and Prospect Theory

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