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Some New Results on Compromise Solutions for Group Decision Problems

Author

Listed:
  • M. Freimer

    (University of Rochester)

  • P. L. Yu

    (The University of Texas, Austin)

Abstract

We report some new results on compromise solutions studied by Yu [Yu, P. L. 1973. A class of decisions for group decision problems. Management Sci. 19 (8, April) 936-946]. The following article focuses on the relation between the compromise solution and its parameter. In particular, we show that, under some nice conditions, the compromise solution is a continuous function of its parameter. A fundamental monotonicity result (Theorem 3.1) concerning compromise solutions is derived. The result enables us to generate the bounds of all compromise solutions. When n = 2, two monotonicity results are derived. These yield a good interpretation of the parameter p. When p is small the "group utility" is emphasized; and when p increases the individual regrets receive more weight. Finally we construct an example to illustrate that the monotonicity results for n = 2 are almost impossible to be generated for n > 2.

Suggested Citation

  • M. Freimer & P. L. Yu, 1976. "Some New Results on Compromise Solutions for Group Decision Problems," Management Science, INFORMS, vol. 22(6), pages 688-693, February.
    • Handle: RePEc:inm:ormnsc:v:22:y:1976:i:6:p:688-693
    DOI: 10.1287/mnsc.22.6.688
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    Cited by:

    1. Strauss, John, 1981. "Social Objective Functions in Agricultural Research," Evaluation of Agricultural Research, Proceedings of a Workshop, Minneapolis, MN, May 12-13, 1980, Miscellaneous Publication 8 49060, University of Minnesota, Agricultural Experiment Station.
    2. Carlos Alós-Ferrer & Jaume García-Segarra & Miguel Ginés-Vilar, 2018. "Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 141-155, October.
    3. de Sousa Xavier, António Manuel & Costa Freitas, Maria de Belém & de Sousa Fragoso, Rui Manuel, 2015. "Management of Mediterranean forests — A compromise programming approach considering different stakeholders and different objectives," Forest Policy and Economics, Elsevier, vol. 57(C), pages 38-46.
    4. Kuldeep Kavta & Arkopal K. Goswami, 2021. "A methodological framework for a priori selection of travel demand management package using fuzzy MCDM methods," Transportation, Springer, vol. 48(6), pages 3059-3084, December.
    5. E Karni & E Werczberger, 1995. "The Compromise Criterion in MCDM: Interpretation and Sensitivity to the p Parameter," Environment and Planning B, , vol. 22(4), pages 407-418, August.
    6. M. Voorneveld & A. Nouweland & R. McLean, 2011. "Axiomatizations of the Euclidean compromise solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 427-448, August.
    7. Torki, Mohammad Mehdi & Hassanajili, Shadi & Jalisi, Marc Mehrzad, 2020. "Design optimizations of PLA stent structure by FEM and investigating its function in a simulated plaque artery," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 103-116.
    8. Büsing, Christina & Goetzmann, Kai-Simon & Matuschke, Jannik & Stiller, Sebastian, 2017. "Reference points and approximation algorithms in multicriteria discrete optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 829-840.
    9. F. Blasco & E. Cuchillo-Ibáñez & M. A. Morón & C. Romero, 1999. "On the Monotonicity of the Compromise Set in Multicriteria Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 69-82, July.
    10. Chi-Yo Huang & Pei-Han Chung & Joseph Z. Shyu & Yao-Hua Ho & Chao-Hsin Wu & Ming-Che Lee & Ming-Jenn Wu, 2018. "Evaluation and Selection of Materials for Particulate Matter MEMS Sensors by Using Hybrid MCDM Methods," Sustainability, MDPI, vol. 10(10), pages 1-35, September.
    11. Claus-Jochen Haake & Cheng-Zhong Qin, 2018. "On unification of solutions to the bargaining problem," Working Papers CIE 113, Paderborn University, CIE Center for International Economics.
    12. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    13. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2007. "Extended VIKOR method in comparison with outranking methods," European Journal of Operational Research, Elsevier, vol. 178(2), pages 514-529, April.
    14. Sankaran, J. K., 1998. "On a variant of lexicographic multi-objective programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 669-674, June.
    15. Stokes, Jeffrey R. & Tozer, Peter R., 2002. "Sire selection with multiple objectives," Agricultural Systems, Elsevier, vol. 73(2), pages 147-164, August.
    16. Hsu, C.-H. & Wang, Fu-Kwun & Tzeng, Gwo-Hshiung, 2012. "The best vendor selection for conducting the recycled material based on a hybrid MCDM model combining DANP with VIKOR," Resources, Conservation & Recycling, Elsevier, vol. 66(C), pages 95-111.
    17. Sebastián Lozano & Narges Soltani & Akram Dehnokhalaji, 2020. "A compromise programming approach for target setting in DEA," Annals of Operations Research, Springer, vol. 288(1), pages 363-390, May.
    18. Li, An-Da & He, Zhen & Wang, Qing & Zhang, Yang, 2019. "Key quality characteristics selection for imbalanced production data using a two-phase bi-objective feature selection method," European Journal of Operational Research, Elsevier, vol. 274(3), pages 978-989.
    19. An, Qingxian & Zhang, Qiaoyu & Tao, Xiangyang, 2023. "Pay-for-performance incentives in benchmarking with quasi S-shaped technology," Omega, Elsevier, vol. 118(C).
    20. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    21. Gwo-Hshiung Tzeng & Chi-Yo Huang, 2012. "Combined DEMATEL technique with hybrid MCDM methods for creating the aspired intelligent global manufacturing & logistics systems," Annals of Operations Research, Springer, vol. 197(1), pages 159-190, August.
    22. Francisco J. André & Carlos Romero, 2006. "On the equivalence between compromise programming and the use of composite compromise metrics," Working Papers 06.33, Universidad Pablo de Olavide, Department of Economics.
    23. Ma, Qiuzhuo & Song, Haiqing & Zhu, Wenbin, 2018. "Low-carbon airline fleet assignment: A compromise approach," Journal of Air Transport Management, Elsevier, vol. 68(C), pages 86-102.
    24. Casiano A. Manrique-de-Lara-Peñate & Dolores R. Santos-Peñate, 2017. "SAM updating using multi-objective optimization techniques," Papers in Regional Science, Wiley Blackwell, vol. 96(3), pages 647-667, August.

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