In this paper,a stable two-sided matching(TSM)method considering the matching intention of agents under a hesitant fuzzy environment is proposed.The method uses a hesitant fuzzy element(HFE)as its basis.First,the HFE ...In this paper,a stable two-sided matching(TSM)method considering the matching intention of agents under a hesitant fuzzy environment is proposed.The method uses a hesitant fuzzy element(HFE)as its basis.First,the HFE preference matrix is transformed into the normalized HFE preference matrix.On this basis,the distance and the projection of the normalized HFEs on positive and negative ideal solutions are calculated.Then,the normalized HFEs are transformed into agent satisfactions.Considering the stable matching constraints,a multiobjective programming model with the objective of maximizing the satisfactions of two-sided agents is constructed.Based on the agent satisfaction matrix,the matching intention matrix of two-sided agents is built.According to the agent satisfaction matrix and matching intention matrix,the comprehensive satisfaction matrix is set up.Furthermore,the multiobjective programming model based on satisfactions is transformed into a multiobjective programming model based on comprehensive satisfactions.Using the G-S algorithm,the multiobjective programming model based on comprehensive satisfactions is solved,and then the best TSM scheme is obtained.Finally,a terminal distribution example is used to verify the feasibility and effectiveness of the proposed method.展开更多
In this paper,we investigate the stable matching problem with multiple preferences in bipartite graphs,where each agent has various preference lists for all available partners with respect to different criteria.The pr...In this paper,we investigate the stable matching problem with multiple preferences in bipartite graphs,where each agent has various preference lists for all available partners with respect to different criteria.The problem requires that each matched agent must have exactly one partner and the obtained matching should be stable for all criteria.As our main contribution,we present an integer linear programming(ILP)model for determining whether there exists a globally stable matching in bipartite graphs,which has been proved to be NP-hard.Since the time consumed for solving ILPs might dramatically increase as the size of instances grows,we develop a preprocessing technique that helps to eliminate pairs that will never be a member of any globally stable matching and thus accelerates the computing process.We perform experiments on randomly generated preference lists and observe a significant speedup when we preprocess the instance before solving the ILPs.As there does not need to exist a perfect matching that is stable for all given criteria,we extend our ILP to the optimized version of the aforementioned problem,which asks to find a matching with maximum cardinality that is stable among all matched agents.展开更多
This paper is focused on the analysis, in the framework of lattice theory, of the matchings obtained from restabilization (after disruption) of stable matchings. When the disruption is due to entry workers or closure ...This paper is focused on the analysis, in the framework of lattice theory, of the matchings obtained from restabilization (after disruption) of stable matchings. When the disruption is due to entry workers or closure of firms the unemployed workers make offers to firms. The stable matching obtained is the firms-worst stable matching of the set of stable matchings that the firms weakly prefer to the initial stable matching (i.e., before being disrupted by changes in the population). More precisely, their position within the lattice of stable matchings is shown.展开更多
We study stable and strongly stable matchings in the marriage market with indifference in their preferences.We characterize the stable matchings as integer extreme points of a convex polytope.We give an alternative pr...We study stable and strongly stable matchings in the marriage market with indifference in their preferences.We characterize the stable matchings as integer extreme points of a convex polytope.We give an alternative proof for the integrity of the strongly stable matching polytope.Also,we compute men-optimal(women-optimal)stable and strongly stable matchings using linear programming.When preferences are strict,we find the men-optimal(women-optimal)stable matching.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.71861015)the Humanities and Social Science Foundation of the Ministry of Education of China (Grant No.18YJA630047)the Distinguished Young Scholar Talent of Jiangxi Province (Grant No.20192BCBL23008).
文摘In this paper,a stable two-sided matching(TSM)method considering the matching intention of agents under a hesitant fuzzy environment is proposed.The method uses a hesitant fuzzy element(HFE)as its basis.First,the HFE preference matrix is transformed into the normalized HFE preference matrix.On this basis,the distance and the projection of the normalized HFEs on positive and negative ideal solutions are calculated.Then,the normalized HFEs are transformed into agent satisfactions.Considering the stable matching constraints,a multiobjective programming model with the objective of maximizing the satisfactions of two-sided agents is constructed.Based on the agent satisfaction matrix,the matching intention matrix of two-sided agents is built.According to the agent satisfaction matrix and matching intention matrix,the comprehensive satisfaction matrix is set up.Furthermore,the multiobjective programming model based on satisfactions is transformed into a multiobjective programming model based on comprehensive satisfactions.Using the G-S algorithm,the multiobjective programming model based on comprehensive satisfactions is solved,and then the best TSM scheme is obtained.Finally,a terminal distribution example is used to verify the feasibility and effectiveness of the proposed method.
基金supported by the National Key R&D Program of China(No.2022YFE0196100)the Guangxi Key Laboratory of Cryptography and Information Security(No.GCIS202116)+2 种基金the Fundamental Research Project of Shenzhen City(No.JCYJ20210324102012033)the Shenzhen Science and Technology Program(No.CJGJZD20210408092806017)the National Natural Science Foundation of China(Nos.12371321 and 12071460).
文摘In this paper,we investigate the stable matching problem with multiple preferences in bipartite graphs,where each agent has various preference lists for all available partners with respect to different criteria.The problem requires that each matched agent must have exactly one partner and the obtained matching should be stable for all criteria.As our main contribution,we present an integer linear programming(ILP)model for determining whether there exists a globally stable matching in bipartite graphs,which has been proved to be NP-hard.Since the time consumed for solving ILPs might dramatically increase as the size of instances grows,we develop a preprocessing technique that helps to eliminate pairs that will never be a member of any globally stable matching and thus accelerates the computing process.We perform experiments on randomly generated preference lists and observe a significant speedup when we preprocess the instance before solving the ILPs.As there does not need to exist a perfect matching that is stable for all given criteria,we extend our ILP to the optimized version of the aforementioned problem,which asks to find a matching with maximum cardinality that is stable among all matched agents.
文摘This paper is focused on the analysis, in the framework of lattice theory, of the matchings obtained from restabilization (after disruption) of stable matchings. When the disruption is due to entry workers or closure of firms the unemployed workers make offers to firms. The stable matching obtained is the firms-worst stable matching of the set of stable matchings that the firms weakly prefer to the initial stable matching (i.e., before being disrupted by changes in the population). More precisely, their position within the lattice of stable matchings is shown.
基金We acknowledge financial support from UNSL(No.032016 and 030320)from Consejo Nacional de Investigaciones Científicas y Técnicas(CONICET)(No.PIP 112-200801-00655)from Agencia Nacional de Promoción Científica y Tecnológica(No.PICT 2017-2355).
文摘We study stable and strongly stable matchings in the marriage market with indifference in their preferences.We characterize the stable matchings as integer extreme points of a convex polytope.We give an alternative proof for the integrity of the strongly stable matching polytope.Also,we compute men-optimal(women-optimal)stable and strongly stable matchings using linear programming.When preferences are strict,we find the men-optimal(women-optimal)stable matching.
