基于属性测度的有差异区间型多准则双边匹配决策方法研究
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摘要
针对具有主体期望水平的有差异区间型多准则双边匹配决策问题,提出了一种基于属性测度的双边匹配决策方法。首先,针对有差异区间型准则,依据属性测度计算各准则值相对于各期望水平的匹配度,并建立双方在各准则下的匹配度矩阵;然后根据简单加权法原则,建立双方综合匹配度矩阵;进一步,根据双方综合匹配度矩阵,以双方主体的匹配度总和最大为目标,构建多目标优化模型,并根据线性加权法将多目标优化模型转换为单目标优化模型,进而通过模型求解得到双边匹配结果;最后,通过实例验证了所提出的双边匹配决策方法的可行性和有效性。
In view of the discrepant interval multi-criteria bilateral matching decision-making problem with subject expectation level,a proposed method has been applied to of the bilateral matching decision-making based on attribute measure.Firstly,the matching degrees of each criterion relative to each expected level can be calculated according to attribute measures with respect to the discrepant interval criteria,thus establishing the matching degree matrix of each criterion.Then,according to the principle of simple weighting method,the comprehensive matching degree matrices of both sides can be established.Furthermore,a multi-objective optimization model is constructed based on the comprehensive matching matrices of both parties and the maximum sum of matching degrees of both parties.By adopting the linear weighted method,the multi-objective optimization model is transformed into a singleobjective optimization model,thus obtaining the bilateral matching results by solving the model.Finally,an example is provided to verify the feasibility and effectiveness of the proposed matching decision method.
In view of the discrepant interval multi-criteria bilateral matching decision-making problem with subject expectation level,a proposed method has been applied to of the bilateral matching decision-making based on attribute measure.Firstly,the matching degrees of each criterion relative to each expected level can be calculated according to attribute measures with respect to the discrepant interval criteria,thus establishing the matching degree matrix of each criterion.Then,according to the principle of simple weighting method,the comprehensive matching degree matrices of both sides can be established.Furthermore,a multi-objective optimization model is constructed based on the comprehensive matching matrices of both parties and the maximum sum of matching degrees of both parties.By adopting the linear weighted method,the multi-objective optimization model is transformed into a singleobjective optimization model,thus obtaining the bilateral matching results by solving the model.Finally,an example is provided to verify the feasibility and effectiveness of the proposed matching decision method.
引文
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[5]陈林,朱卫平.基于二手市场与理性预期的房地产市场机制研究[J].管理科学学报,2011,14(2):61-70.CHEN Lin,ZHU Weiping.Research on Real Estate Market Mechanism in the Second-Hand Market and Rational Expectation[J].Journal of Management Sciences in China,2011,14(2):61-70.
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[7]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 Xi,FAN Zhiping.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.
[8]GABAIX X,LANDIER A.Why Has CEO Pay Increased so Much[J].Quarterly Journal of Economics,2008,123(1):49-100.
[9]GINSBURG T,WOLF J A.The Market for Elite Law Firm Associates[J].The Florida State University Law Review,2003,31(1):909-963.
[10]樊治平,乐琦.基于完全偏好序信息的严格双边匹配方法[J].管理科学学报,2014,17(1):21-34.FAN Zhiping,YUE Qi.Strict Two-Sided Matching Method Based on Complete Preference Ordinal Information[J].Journal of Management Sciences in China,2014,17(1):21-34.
[11]梁海明,姜艳萍.一种基于弱偏好序信息的双边匹配决策方法[J].系统工程学报,2014,29(2):153-159.LIANG Haiming,JIANG Yanping.Method for TwoSided Matching Decision-Making Based on the Weak Preference Ordering Information[J].Journal of Systems Engineering,2014,29(2):153-159.
[12]李铭洋,樊治平.考虑双方主体心理行为的稳定双边匹配方法[J].系统工程理论与实践,2014,34(10):2591-2599.LI Mingyang,FAN Zhiping.Method for Stable TwoSided Matching Considering Psychological Behavior of Agents on Both Sides[J].Systems Engineering-Theory&Practice,2014,34(10):2591-2599.
[13]乐琦,樊治平.基于累积前景理论的双边匹配决策方法[J].系统工程学报,2013,28(1):38-46.YUE Qi,FAN Zhiping.Decision Method for Two-Sided Matching Based on Cumulative Prospect Theory[J].Journal of Systems Engineering,2013,28(1):38-46.
[14]乐琦,樊治平.一种具有序值信息的双边匹配决策方法[J].系统工程学报,2012,27(2):185-192.YUE Qi,FAN Zhiping.Method for Two-Sided Matching Decision-Making with Ordinal Numbers[J].Journal of Systems Engineering,2012,27(2):185-192.
[15]乐琦.基于累积前景理论的具有不确定偏好序信息的双边匹配决策方法[J].系统科学与数学,2013,33(9):1061-1070.YUE Qi.Decision Method for the Two-Sided Matching with Uncertain Preference Ordinal Information Based on Cumulative Prospect Theory[J].Journal of Systems Science and Mathematical Sciences,2013,33(9):1061-1070.
[16]乐琦.基于不完全序关系信息的双边匹配决策方法[J].浙江大学学报(理学版),2014,41(5):523-527.YUE Qi.Decision Method for Two-Sided Mathching Based on Incomplete Order Relation Information[J].Journal of Zhejiang University(Science Edition),2014,41(5):523-527.
[17]乐琦.基于累积前景理论的具有不完全序值信息的双边匹配决策方法[J].运筹与管理,2013,22(4):26-32.YUE Qi.Decision Method for Two-Sided Matching with Incomplete Ordinal Number Information Based on Cumulative Prospect Theory[J].Operations Research and Management Science,2013,22(4):26-32.
[18]SIM K M,CHAN R.A Brokering Protocol for AgentBased E-Commerce[J].IEEE Transaction on Systems,Man,and Cybernetics,Part C:Applications and Reviews,2000,30(4):474-484.
[19]蒋忠中,樊治平,汪定伟.电子中介中具有模糊信息且需求不可分的多属性商品交易匹配问题[J].系统工程理论与实践,2011,31(12):2355-2366.JIANG Zhongzhong,FAN Zhiping,WANG Dingwei.Trade Matching for Multi-Attribute Exchanges with Fuzzy Information and Indivisible Demand in E-Brokerage[J].Systems Engineering-Theory&Practice,2011,31(12):2355-2366.
[20]蒋忠中,樊治平,汪定伟,等.具模糊信息的多数量多属性电子交易匹配问题[J].管理科学学报,2014,17(5):52-65.JIANG Zhongzhong,FAN Zhiping,WANG Dingwei,et al.Matching Model and Algorithm for Multi-Unit Multi-Attribute Exchanges with Fuzzy Information in E-Brokerage[J].Journal of Management Sciences in China,2014,17(5):52-65.
[21]HUYNH V N,NAKAMORI Y.A Satisfactory-Oriented Approach to Multiexpert Decision-Making with Linguistic Assessments[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2005,35(2):184-196.
[22]陈希,樊治平.电子采购中具有语言评价信息的交易匹配问题研究[J].运筹与管理,2009,18(3):132-137.CHEN Xi,FAN Zhiping.Research on Trade Matching Problem in Electronic Procurement with Linguistic Assessment Information[J].Operations Research and Management Science,2009,18(3):132-137.
[23]陈希,韩菁,张晓.考虑心理期望与感知的多属性匹配决策方法[J].控制与决策,2014,29(11):2027-2033.CHEN Xi,HAN Jing,ZHANG Xiao.Method for Multiple Attribute Matching Decision Making Considering Matching Body's Psychological Aspiration and Perception[J].Control and Decision,2014,29(11):2027-2033.
[24]万树平,李登峰.具有不同类型信息的风险投资商与投资企业多指标双边匹配决策方法[J].中国管理科学,2014,22(2):40-47.WAN Shuping,LI Dengfeng.Decision Making Method for Multi-Attribute Two-Side Matching Problem Between Venture Capitalists and Investment Enterprises with Different Kinds of Information[J].Chinese Journal of Management Science,2014,22(2):40-47.
[25]乐琦.基于前景理论的相同无差异区间型多指标匹配决策方法[J].系统科学与数学,2013,33(12):1447-1455.YUE Qi.The Same Indifference Interval Multiple Criteria Matching Decision Method Based on Prospect Theory[J].Journal of Systems Science and Mathematical Sciences,2013,33(12):1447-1455.
[26]乐琦.无差异区间型多指标匹配决策方法[J].系统工程学报,2014,29(1):41-47.YUE Qi.Indifference Interval Multiple Criteria Matching Decision Method[J].Journal of Systems Engineering,2014,29(1):41-47.
[27]程乾生.属性识别理论模型及其应用[J].北京大学学报(自然科学版),1997,33(1):12-20.CHENG Qiansheng.Attribute Recognition Theoretical Model with Application[J].Acta Scientiarum Naturalium Universitatis Pekinensis,1997,33(1):12-20.
[28]程乾生.属性数学:属性测度和属性统计[J].数学的实践与认识,1998,28(2):97-107.CHENG Qiansheng.Attribute Mathematics:Attribute Measure and Attribute Statistics[J].Mthematics in Practice and Theory,1998,28(2):97-107.
[29]ROTH A E.Common and Conflicting Interests in Two-Sided Matching Markets[J].European Economic Review,1985,27(1):75-96.
[2]GUSFIELD D,IRVING R W.The Stable Marriage Problem,Structure and Algorithms[M].Cambridge:MITPress,1989:56-102.
[3]PAIS J.Random Matching in the College Admissions Problem[J].Economic Theory,2008,35(1):99-116.
[4]聂海峰.高考录取机制的博弈分析[J].经济学(季刊),2007,6(3):899-916.NIE Haifeng.A Game Theoretical Analysis of China's College Admission Mechanism[J].China Economic Quarterly,2007,6(3):899-916.
[5]陈林,朱卫平.基于二手市场与理性预期的房地产市场机制研究[J].管理科学学报,2011,14(2):61-70.CHEN Lin,ZHU Weiping.Research on Real Estate Market Mechanism in the Second-Hand Market and Rational Expectation[J].Journal of Management Sciences in China,2011,14(2):61-70.
[6]GOODMAN S A,SVYANTEK D J.Person-Organization Fit and Contextual Performance:Do Shared Values Matter[J].Journal of Vocational Behavior,1999,55(2):254-275.
[7]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 Xi,FAN Zhiping.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.
[8]GABAIX X,LANDIER A.Why Has CEO Pay Increased so Much[J].Quarterly Journal of Economics,2008,123(1):49-100.
[9]GINSBURG T,WOLF J A.The Market for Elite Law Firm Associates[J].The Florida State University Law Review,2003,31(1):909-963.
[10]樊治平,乐琦.基于完全偏好序信息的严格双边匹配方法[J].管理科学学报,2014,17(1):21-34.FAN Zhiping,YUE Qi.Strict Two-Sided Matching Method Based on Complete Preference Ordinal Information[J].Journal of Management Sciences in China,2014,17(1):21-34.
[11]梁海明,姜艳萍.一种基于弱偏好序信息的双边匹配决策方法[J].系统工程学报,2014,29(2):153-159.LIANG Haiming,JIANG Yanping.Method for TwoSided Matching Decision-Making Based on the Weak Preference Ordering Information[J].Journal of Systems Engineering,2014,29(2):153-159.
[12]李铭洋,樊治平.考虑双方主体心理行为的稳定双边匹配方法[J].系统工程理论与实践,2014,34(10):2591-2599.LI Mingyang,FAN Zhiping.Method for Stable TwoSided Matching Considering Psychological Behavior of Agents on Both Sides[J].Systems Engineering-Theory&Practice,2014,34(10):2591-2599.
[13]乐琦,樊治平.基于累积前景理论的双边匹配决策方法[J].系统工程学报,2013,28(1):38-46.YUE Qi,FAN Zhiping.Decision Method for Two-Sided Matching Based on Cumulative Prospect Theory[J].Journal of Systems Engineering,2013,28(1):38-46.
[14]乐琦,樊治平.一种具有序值信息的双边匹配决策方法[J].系统工程学报,2012,27(2):185-192.YUE Qi,FAN Zhiping.Method for Two-Sided Matching Decision-Making with Ordinal Numbers[J].Journal of Systems Engineering,2012,27(2):185-192.
[15]乐琦.基于累积前景理论的具有不确定偏好序信息的双边匹配决策方法[J].系统科学与数学,2013,33(9):1061-1070.YUE Qi.Decision Method for the Two-Sided Matching with Uncertain Preference Ordinal Information Based on Cumulative Prospect Theory[J].Journal of Systems Science and Mathematical Sciences,2013,33(9):1061-1070.
[16]乐琦.基于不完全序关系信息的双边匹配决策方法[J].浙江大学学报(理学版),2014,41(5):523-527.YUE Qi.Decision Method for Two-Sided Mathching Based on Incomplete Order Relation Information[J].Journal of Zhejiang University(Science Edition),2014,41(5):523-527.
[17]乐琦.基于累积前景理论的具有不完全序值信息的双边匹配决策方法[J].运筹与管理,2013,22(4):26-32.YUE Qi.Decision Method for Two-Sided Matching with Incomplete Ordinal Number Information Based on Cumulative Prospect Theory[J].Operations Research and Management Science,2013,22(4):26-32.
[18]SIM K M,CHAN R.A Brokering Protocol for AgentBased E-Commerce[J].IEEE Transaction on Systems,Man,and Cybernetics,Part C:Applications and Reviews,2000,30(4):474-484.
[19]蒋忠中,樊治平,汪定伟.电子中介中具有模糊信息且需求不可分的多属性商品交易匹配问题[J].系统工程理论与实践,2011,31(12):2355-2366.JIANG Zhongzhong,FAN Zhiping,WANG Dingwei.Trade Matching for Multi-Attribute Exchanges with Fuzzy Information and Indivisible Demand in E-Brokerage[J].Systems Engineering-Theory&Practice,2011,31(12):2355-2366.
[20]蒋忠中,樊治平,汪定伟,等.具模糊信息的多数量多属性电子交易匹配问题[J].管理科学学报,2014,17(5):52-65.JIANG Zhongzhong,FAN Zhiping,WANG Dingwei,et al.Matching Model and Algorithm for Multi-Unit Multi-Attribute Exchanges with Fuzzy Information in E-Brokerage[J].Journal of Management Sciences in China,2014,17(5):52-65.
[21]HUYNH V N,NAKAMORI Y.A Satisfactory-Oriented Approach to Multiexpert Decision-Making with Linguistic Assessments[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2005,35(2):184-196.
[22]陈希,樊治平.电子采购中具有语言评价信息的交易匹配问题研究[J].运筹与管理,2009,18(3):132-137.CHEN Xi,FAN Zhiping.Research on Trade Matching Problem in Electronic Procurement with Linguistic Assessment Information[J].Operations Research and Management Science,2009,18(3):132-137.
[23]陈希,韩菁,张晓.考虑心理期望与感知的多属性匹配决策方法[J].控制与决策,2014,29(11):2027-2033.CHEN Xi,HAN Jing,ZHANG Xiao.Method for Multiple Attribute Matching Decision Making Considering Matching Body's Psychological Aspiration and Perception[J].Control and Decision,2014,29(11):2027-2033.
[24]万树平,李登峰.具有不同类型信息的风险投资商与投资企业多指标双边匹配决策方法[J].中国管理科学,2014,22(2):40-47.WAN Shuping,LI Dengfeng.Decision Making Method for Multi-Attribute Two-Side Matching Problem Between Venture Capitalists and Investment Enterprises with Different Kinds of Information[J].Chinese Journal of Management Science,2014,22(2):40-47.
[25]乐琦.基于前景理论的相同无差异区间型多指标匹配决策方法[J].系统科学与数学,2013,33(12):1447-1455.YUE Qi.The Same Indifference Interval Multiple Criteria Matching Decision Method Based on Prospect Theory[J].Journal of Systems Science and Mathematical Sciences,2013,33(12):1447-1455.
[26]乐琦.无差异区间型多指标匹配决策方法[J].系统工程学报,2014,29(1):41-47.YUE Qi.Indifference Interval Multiple Criteria Matching Decision Method[J].Journal of Systems Engineering,2014,29(1):41-47.
[27]程乾生.属性识别理论模型及其应用[J].北京大学学报(自然科学版),1997,33(1):12-20.CHENG Qiansheng.Attribute Recognition Theoretical Model with Application[J].Acta Scientiarum Naturalium Universitatis Pekinensis,1997,33(1):12-20.
[28]程乾生.属性数学:属性测度和属性统计[J].数学的实践与认识,1998,28(2):97-107.CHENG Qiansheng.Attribute Mathematics:Attribute Measure and Attribute Statistics[J].Mthematics in Practice and Theory,1998,28(2):97-107.
[29]ROTH A E.Common and Conflicting Interests in Two-Sided Matching Markets[J].European Economic Review,1985,27(1):75-96.
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