Advertisement

An enhanced approach for two-sided matching with 2-tuple linguistic multi-attribute preference

  • Yang Lin
  • Ying-Ming Wang
  • Kwai-Sang Chin
Methodologies and Application

Abstract

This paper focuses on multi-attribute two-sided matching with 2-tuple preferences. A new framework consisting of paring process and feedback process is proposed to generate matching results (couples) in multiple stages. According to the assumption that matching couples should be satisfied with each other, the concept of expected matching ordinal (EMO) is defined and used for filtering unqualified couples in each stage. To derive optimal results, payoff matrices and preference ordinals are firstly obtained on the basis of the preferences given by two-sided players. The paring process formulates a bi-objective optimization model to generate primary matching couples based on the payoff matrices. Subsequently, the feedback process identifies targeted couples from them with the EMO constraint. This mechanism is performed to ensure that matching couples are all mutually satisfied. The novelty of our approach is that we manage matching decisions by balancing individual benefit and party’s benefit. Finally, a practical example is given to illustrate the proposed approach and comparison analysis shows the advantages of our approach. Some related issues are further discussed.

Keywords

Two-sided matching 2-Tuple linguistic Preference ordinal Feedback mechanism Optimization 

Notes

Acknowledgements

The authors are very grateful to editor in chief and anonymous referees for their insightful and constructive comments and suggestions that have led to an improved version of this paper. The work was partly supported by the National Natural Science Foundation of China (61773123), the Humanities and Social Sciences Foundation of Ministry of Education of China (16YJC630008).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Abdulkadiroğlu A, Sönmez T (1998) Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica 66(3):689–701MathSciNetCrossRefzbMATHGoogle Scholar
  2. Abdulkadiroğlu A, Sönmez T (1999) House allocation with existing tenants. J Econ Theory 88(2):233–260CrossRefzbMATHGoogle Scholar
  3. Azevedo EM (2014) Imperfect competition in two-sided matching markets. Games Econ Behav 83:207–223MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bertoni F, Colombo MG, Grilli L (2011) Venture capital financing and the growth of high-tech start-ups: disentangling treatment from selection effects. Res Policy 40(7):1028–1043CrossRefGoogle Scholar
  5. Chen X, Li Z, Fan ZP, Zhou X, Zhang X (2016) Matching demanders and suppliers in knowledge service: a method based on fuzzy axiomatic design. Inf Sci 346–347:130–145MathSciNetCrossRefGoogle Scholar
  6. Cook WD, Kress M (1985) Ordinal ranking with intensity of preference. Manag Sci 31(1):26–32MathSciNetCrossRefzbMATHGoogle Scholar
  7. Dong YC, Zhang GQ, Hong WC, Yu S (2013) Linguistic computational model based on 2-tuples and intervals. IEEE Trans Fuzzy Syst 21(6):1006–1018CrossRefGoogle Scholar
  8. Dong YC, Li CC, Xu YF, Gu X (2015) Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations. Group Decis Negot 24(2):217–242CrossRefGoogle Scholar
  9. Echenique F, Galichon A (2017) Ordinal and cardinal solution concepts for two-sided matching. Games Econ Behav 101:63–77MathSciNetCrossRefzbMATHGoogle Scholar
  10. Fan ZP, Yue Q, Feng B (2010) An approach to group decision-making with uncertain preference ordinals. Comput Ind Eng 58(1):51–57CrossRefGoogle Scholar
  11. Fan ZP, Li MY, Yue Q (2014) Decision analysis method for two-sided satisfied matching considering stable matching condition. Chin J Manag Sci 22(4):112–118Google Scholar
  12. Fan ZP, Li MY, Zhang X (2017) Satisfied two-sided matching: a method considering elation and disappointment of agents. Soft Comput.  https://doi.org/10.1007/s00500-017-2725-1 Google Scholar
  13. Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69(1):9–15MathSciNetCrossRefzbMATHGoogle Scholar
  14. Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115(1):67–82MathSciNetCrossRefzbMATHGoogle Scholar
  15. Herrera F, Martinez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):8746–8752Google Scholar
  16. Hwang HS, Ko WH, Goan MJ (2007) Web-based multi-attribute analysis model for make-or-buy decisions. Math Comput Model 46(7):1081–1090MathSciNetCrossRefGoogle Scholar
  17. Jiang ZZ, Fan ZP, Ip WH, Chen XH (2016) Fuzzy multi-objective modeling and optimization for one-shot multi-attribute exchanges with indivisible demand. IEEE Trans Fuzzy Syst 24(3):708–723CrossRefGoogle Scholar
  18. Ju Y, Liu X, Wang A (2016) Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making. Soft Comput 20(10):4037–4053CrossRefzbMATHGoogle Scholar
  19. Lawson C (1999) Towards a competence theory of the region. Camb J Econ 23(2):151–166CrossRefGoogle Scholar
  20. Lin Y, Wang YM, Chen SQ (2017) Hesitant fuzzy multi-attribute matching decision making based on regret theory with uncertain weights. Int J Fuzzy Syst 19(4):955–966MathSciNetCrossRefGoogle Scholar
  21. Liu Y (2014) A method for 2-tuple linguistic dynamic multiple attribute decision making with entropy weight. J Intell Fuzzy Syst 27(4):1803–1810MathSciNetzbMATHGoogle Scholar
  22. Martinez L, Herrera F (2012) An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf Sci 207(1):1–18MathSciNetCrossRefGoogle Scholar
  23. Neumann JLV, Morgenstern OV (1947) Theory of games and economic behavior. Princeton University Press, PrincetonzbMATHGoogle Scholar
  24. Pang Q, Wang H, Xu ZS (2016) Probabilistic linguistic term sets in multiattribute group decision making. Inf Sci 369:128–143CrossRefGoogle Scholar
  25. Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119CrossRefGoogle Scholar
  26. Roth AE (1982) The economics of matching: stability and incentives. Math Oper Res 7(4):617–628MathSciNetCrossRefzbMATHGoogle Scholar
  27. Roth AE, Rothblum UG, Vande Vate JH (1993) Stable matching, optimal assignments and linear programming. Math Oper Res 18(4):803–828MathSciNetCrossRefzbMATHGoogle Scholar
  28. Shapley LS, Shubik M (1971) The assignment game I: the core. Int J Game Theory 1(1):111–130MathSciNetCrossRefzbMATHGoogle Scholar
  29. Sotomayor M (1999) Three remarks on the many-to-many stable matching problem. Math Soc Sci 38(1):55–70CrossRefzbMATHGoogle Scholar
  30. Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297–323CrossRefzbMATHGoogle Scholar
  31. Wan SP, Li DF (2013) Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information. Appl Soft Comput 13(11):4333–4348CrossRefGoogle Scholar
  32. Wang P, Shen J, Zhang B (2016) A new method for two-sided matching decision making of PPP projects based on intuitionistic fuzzy Choquet integral. J Intell Fuzzy Syst 31(4):2221–2230CrossRefGoogle Scholar
  33. Wang X, Agatz N, Erera A (2017) Stable matching for dynamic ride-sharing systems. Transp Sci.  https://doi.org/10.1287/trsc.2017.0768 zbMATHGoogle Scholar
  34. Wei LJ (2011) Optimal mechanism design of weak preference orders one-sided matching. Syst Eng Theory Pract 31(9):1687–1695Google Scholar
  35. Xu ZS (2004) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166(1):19–30MathSciNetCrossRefzbMATHGoogle Scholar
  36. Yue Q, Fan ZP (2012) Method for two-sided matching decision making with ordinal numbers. J Syst Eng 27(2):150–159zbMATHGoogle Scholar
  37. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8(3):199–249MathSciNetCrossRefzbMATHGoogle Scholar
  38. Zhou YY (2016) Bayesian estimation of a dynamic model of two-sided markets: application to the US video game industry. Manag Sci 63(11):3874–3894CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Decision Sciences InstituteFuzhou UniversityFuzhouChina
  2. 2.Key Laboratory of Spatial Data Mining and Information Sharing of Ministry of EducationFuzhou UniversityFuzhouChina
  3. 3.School of EconomicsFujian Normal UniversityFuzhouChina
  4. 4.Department of Systems Engineering and Engineering ManagementCity University of Hong KongKowloon TongHong Kong

Personalised recommendations