IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v207y2010i1p371-379.html
   My bibliography  Save this article

Set choice problems with incomplete information about the preferences of the decision maker

Author

Listed:
  • Podinovski, Vladislav V.

Abstract

We consider the problem of selecting a predetermined number of objects from a given finite set. It is assumed that the preferences of the decision maker on this set are only partially known. Our solution approach is based on the notions of optimal and non-dominated subsets. The properties of such subsets and the objects they contain are investigated. The implementation of the developed approach is discussed and illustrated by various examples.

Suggested Citation

  • Podinovski, Vladislav V., 2010. "Set choice problems with incomplete information about the preferences of the decision maker," European Journal of Operational Research, Elsevier, vol. 207(1), pages 371-379, November.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:371-379
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00309-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fishburn, Peter C., 1992. "Signed orders and power set extensions," Journal of Economic Theory, Elsevier, vol. 56(1), pages 1-19, February.
    2. Heiner, Ronald A. & Packard, Dennis J., 1984. "A uniqueness result for extending orders; with application to collective choice as inconsistency resolution," Journal of Economic Theory, Elsevier, vol. 32(1), pages 180-184, February.
    3. Edwards, Ward & Barron, F. Hutton, 1994. "SMARTS and SMARTER: Improved Simple Methods for Multiattribute Utility Measurement," Organizational Behavior and Human Decision Processes, Elsevier, vol. 60(3), pages 306-325, December.
    4. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    5. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    6. Carrizosa, E. & Conde, E. & Fernandez, F. R. & Puerto, J., 1995. "Multi-criteria analysis with partial information about the weighting coefficients," European Journal of Operational Research, Elsevier, vol. 81(2), pages 291-301, March.
    7. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, September.
    8. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    9. Podinovski, Vladislav V., 2007. "Interval articulation of superiority and precise elicitation of priorities," European Journal of Operational Research, Elsevier, vol. 180(1), pages 406-417, July.
    10. Fishburn, Peter C. & LaValle, Irving H., 1996. "Binary interactions and subset choice," European Journal of Operational Research, Elsevier, vol. 92(1), pages 182-192, July.
    11. Gordon B. Hazen, 1986. "Partial Information, Dominance, and Potential Optimality in Multiattribute Utility Theory," Operations Research, INFORMS, vol. 34(2), pages 296-310, April.
    12. Cook, Wade D. & Kress, Moshe, 1991. "A multiple criteria decision model with ordinal preference data," European Journal of Operational Research, Elsevier, vol. 54(2), pages 191-198, September.
    13. Solymosi, Tamas & Dombi, Jozsef, 1986. "A method for determining the weights of criteria: The centralized weights," European Journal of Operational Research, Elsevier, vol. 26(1), pages 35-41, July.
    14. Bossert, Walter, 1989. "On the extension of preferences over a set to the power set: An axiomatic characterization of a quasi-ordering," Journal of Economic Theory, Elsevier, vol. 49(1), pages 84-92, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Cinelli, Marco & Kadziński, Miłosz & Gonzalez, Michael & Słowiński, Roman, 2020. "How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy," Omega, Elsevier, vol. 96(C).
    2. Podinovski, Vladislav V., 2013. "Non-dominance and potential optimality for partial preference relations," European Journal of Operational Research, Elsevier, vol. 229(2), pages 482-486.
    3. Harju, Mikko & Liesiö, Juuso & Virtanen, Kai, 2019. "Spatial multi-attribute decision analysis: Axiomatic foundations and incomplete preference information," European Journal of Operational Research, Elsevier, vol. 275(1), pages 167-181.
    4. Chang, Ching-Ter, 2011. "Multi-choice goal programming with utility functions," European Journal of Operational Research, Elsevier, vol. 215(2), pages 439-445, December.
    5. Xiaoyue Liu & Dawei Ju, 2021. "Hesitant Fuzzy 2-Dimension Linguistic Programming Technique for Multidimensional Analysis of Preference for Multicriteria Group Decision Making," Mathematics, MDPI, vol. 9(24), pages 1-23, December.
    6. Chun-xiang Guo & Ying Peng, 2015. "Lattice Order Group Decision Making with Interval Probability Based on Prospect Theory," Group Decision and Negotiation, Springer, vol. 24(5), pages 753-775, September.
    7. Wan, Shu-Ping & Li, Deng-Feng, 2013. "Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees," Omega, Elsevier, vol. 41(6), pages 925-940.
    8. Deng-Feng Li & Shu-Ping Wan, 2017. "Minimum Weighted Minkowski Distance Power Models for Intuitionistic Fuzzy Madm with Incomplete Weight Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1387-1408, September.
    9. Cinelli, Marco & Kadziński, Miłosz & Miebs, Grzegorz & Gonzalez, Michael & Słowiński, Roman, 2022. "Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system," European Journal of Operational Research, Elsevier, vol. 302(2), pages 633-651.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Ahn, Byeong Seok, 2017. "Approximate weighting method for multiattribute decision problems with imprecise parameters," Omega, Elsevier, vol. 72(C), pages 87-95.
    3. Walter Bossert, 1998. "Opportunity Sets and the Measurement of Information," Discussion Papers 98/6, University of Nottingham, School of Economics.
    4. Bossert, Walter, 1997. "Uncertainty aversion in nonprobabilistic decision models," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 191-203, October.
    5. Dinko Dimitrov & Ruud Hendrickx & Peter Borm, 2004. "Good and bad objects: the symmetric difference rule," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-7.
    6. Fishburn, Peter C. & LaValle, Irving H., 1996. "Binary interactions and subset choice," European Journal of Operational Research, Elsevier, vol. 92(1), pages 182-192, July.
    7. Bossert, Walter, 2000. "Opportunity sets and uncertain consequences1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 475-496, May.
    8. Dimitrov, D.A. & Borm, P.E.M. & Hendrickx, R.L.P., 2003. "Good and Bad Objects : Cardinality-Based Rules," Other publications TiSEM be8831b3-40d4-4af0-93d3-4, Tilburg University, School of Economics and Management.
    9. Salo, Ahti A., 1995. "Interactive decision aiding for group decision support," European Journal of Operational Research, Elsevier, vol. 84(1), pages 134-149, July.
    10. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 227-245, March.
    11. Sam Park, Kyung & Sang Lee, Kyung & Seong Eum, Yun & Park, Kwangtae, 2001. "Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information," European Journal of Operational Research, Elsevier, vol. 134(3), pages 557-563, November.
    12. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 729-741, October.
    13. Salvador Barberà & Danilo Coelho, 2008. "How to choose a non-controversial list with k names," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 79-96, June.
    14. Xu, Xiaozhan & Martel, Jean-Marc & Lamond, Bernard F., 2001. "A multiple criteria ranking procedure based on distance between partial preorders," European Journal of Operational Research, Elsevier, vol. 133(1), pages 69-80, August.
    15. Selçuk Özyurt & M. Sanver, 2008. "Strategy-proof resolute social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 89-101, January.
    16. Salo, Ahti & Punkka, Antti, 2005. "Rank inclusion in criteria hierarchies," European Journal of Operational Research, Elsevier, vol. 163(2), pages 338-356, June.
    17. Emre Doğan & M. Sanver, 2008. "Arrovian impossibilities in aggregating preferences over non-resolute outcomes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 495-506, April.
    18. BOSSERT, Walter & SLINKO, Arkadii, 2004. "Relative Uncertainty and Additively Representable Set Rankings," Cahiers de recherche 2004-13, Universite de Montreal, Departement de sciences economiques.
    19. A Mateos & S Ríos-Insua & A Jiménez, 2007. "Dominance, potential optimality and alternative ranking in imprecise multi-attribute decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 326-336, March.
    20. Ritxar Arlegi, 2001. "Rational Evaluation of Actions Under Complete Uncertainty," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0114, Departamento de Economía - Universidad Pública de Navarra.

    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:eee:ejores:v:207:y:2010:i:1:p:371-379. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.