IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v22y1976i6p688-693.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.22.6.688
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.22.6.688?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. Stokes, Jeffrey R. & Tozer, Peter R., 2002. "Sire selection with multiple objectives," Agricultural Systems, Elsevier, vol. 73(2), pages 147-164, August.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    12. 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.
    13. 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.
    14. 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.
    15. An, Qingxian & Zhang, Qiaoyu & Tao, Xiangyang, 2023. "Pay-for-performance incentives in benchmarking with quasi S-shaped technology," Omega, Elsevier, vol. 118(C).
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:22:y:1976:i:6:p:688-693. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.