基于概率犹豫模糊信息的三边单向非循环稳定匹配  

Three-sided Unidirectional Acyclic Stable Matchings Based on Probabilistic Hesitant Fuzzy Information

作　　者：杨洋[1,2] 赵晓冬[1] YANG Yang;ZHAO Xiao-dong(College of Economics and Management,Yanshan University,Qinhuangdao 066004,China;Liren College,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学经济管理学院,河北秦皇岛066004 [2]燕山大学里仁学院,河北秦皇岛066004

出　　处：《模糊系统与数学》2020年第3期48-59,共12页Fuzzy Systems and Mathematics

基　　金：教育部人文社会科学青年基金资助项目(19YJCZH234);河北省社会科学基金年度项目(HB19GL009);河北省自然科学基金资助项目(F2018203370)。

摘　　要：本文针对单向非循环偏好下的三边匹配问题,基于概率犹豫模糊偏好信息,提出了一种稳定匹配算法。首先,针对三边单向非循环匹配问题,给出了概率犹豫模糊偏好元及其相对期望得分、相对偏差的定义,建立了对主体偏好排序的三级排序法;然后,基于三边主体偏好序,以匹配基数最大化及稳定匹配为目标,建立了三边单向非循环匹配的数学模型;进一步地,提出了阈值约束条件下的两阶段搜索优选算法,并对算法输出匹配的稳定性进行了证明;最后,通过一个实例验证本文所提算法的可行性和有效性。A stable matching algorithm based on probabilistic hesitation fuzzy preference information is proposed for three-sided matching problem with unidirectional acyclic preference.Firstly,for the three-sided one-way acyclic matching problem,the definitions of probabilistic hesitant fuzzy preference element and its relative expected score and relative deviation are given,and the three-level sorting method is established.Then,based on the preference order,the mathematical model for three-sided unidirectional acyclic matching is established with the goal of maximizing matching cardinality.Furthermore,an edge-by-edge optimization algorithm in two-stage with the threshold constraints is proposed,and the stability of the output scheme is proved respectively.Finally,an example is given to verify the feasibility and effectiveness of the proposed algorithm.

关 键 词：三边匹配 非循环偏好 稳定性 概率犹豫模糊集 

分 类 号：C934[经济管理—管理学]