IDEAS home Printed from https://ideas.repec.org/a/spr/fuzodm/v17y2018i3d10.1007_s10700-017-9272-1.html
   My bibliography  Save this article

On a correspondence between probabilistic and fuzzy choice functions

Author

Listed:
  • Davide Martinetti

    (University of Oviedo)

  • Susana Montes

    (University of Oviedo)

  • Susana Díaz

    (University of Oviedo)

  • Bernard Baets

    (Ghent University)

Abstract

Probabilistic and fuzzy choice functions are used to describe decision situations in which some degree of uncertainty or imprecision is involved. We propose a way to equate these two formalisms by means of residual implication operations. Furthermore, a set of new rationality conditions for probabilistic choice functions is proposed and proved to be sufficient to ensure that the associated fuzzy choice function is rational.

Suggested Citation

  • Davide Martinetti & Susana Montes & Susana Díaz & Bernard Baets, 2018. "On a correspondence between probabilistic and fuzzy choice functions," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 247-264, September.
  • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:3:d:10.1007_s10700-017-9272-1
    DOI: 10.1007/s10700-017-9272-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10700-017-9272-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10700-017-9272-1?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
    ---><---

    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. Indraneel Dasgupta, 2011. "Contraction consistent stochastic choice correspondence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 643-658, October.
    2. Shasikanta Nandeibam, 2011. "On randomized rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 633-641, October.
    3. Bandyopadhyay, Taradas & Bandyopadhyay, Bandyopadhyay & Pattanaik, Prasanta K., 2002. "Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference," Journal of Economic Theory, Elsevier, vol. 107(2), pages 483-489, December.
    4. Gregory Richardson, 1998. "The structure of fuzzy preferences: Social choice implications," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 359-369.
    5. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    6. Indraneel Dasgupta & Prasanta Pattanaik, 2007. "‘Regular’ choice and the weak axiom of stochastic revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 35-50, April.
    7. Bandyopadhyay, Taradas & Dasgupta, Indraneel & Pattanaik, Prasanta K., 1999. "Stochastic Revealed Preference and the Theory of Demand," Journal of Economic Theory, Elsevier, vol. 84(1), pages 95-110, January.
    8. Taradas Bandyopadhyay & Indraneel Dasgupta & Prasanta Pattanaik, 2004. "A general revealed preference theorem for stochastic demand behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 589-599, March.
    9. Shasikanta Nandeibam, 2009. "On probabilistic rationalizability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 425-437, March.
    10. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    11. Kunal Sengupta, 1999. "Choice rules with fuzzy preferences: Some characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 259-272.
    Full references (including those not matched with items on IDEAS)

    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. Indraneel Dasgupta, 2011. "Contraction consistent stochastic choice correspondence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 643-658, October.
    2. Dasgupta Indraneel & Pattanaik P. K, 2010. "Revealed Preference with Stochastic Demand Correspondence," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, August.
    3. Jan Heufer, 2011. "Stochastic revealed preference and rationalizability," Theory and Decision, Springer, vol. 71(4), pages 575-592, October.
    4. Dasgupta Indraneel, 2009. "Supply Theory sans Profit Maximization," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-16, July.
    5. Jan Heufer, 2009. "Stochastic homothetically revealed preference for tight stochastic demand functions," Economics Bulletin, AccessEcon, vol. 29(3), pages 2472-2477.
    6. Heufer, Jan, 2013. "Quasiconcave preferences on the probability simplex: A nonparametric analysis," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 21-30.
    7. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    8. Indraneel Dasgupta, 2005. "Consistent firm choice and the theory of supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 167-175, July.
    9. WILLIAM J. McCAUSLAND, 2009. "Random Consumer Demand," Economica, London School of Economics and Political Science, vol. 76(301), pages 89-107, February.
    10. José Alcantud, 2006. "Notes and Comments: Stochastic demand correspondences and their aggregation properties," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 29(1), pages 55-69, May.
    11. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.
    12. Kovács, Máté, 2009. "Kinyilvánított preferencia és racionalitás [Declared preference and rationality]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 546-562.
    13. J. C. R. Alcantud, 2003. "Stochastic demand correspondences and their aggregation properties," Microeconomics 0309001, University Library of Munich, Germany, revised 08 Jan 2005.
    14. Richter, Marcel K. & Wong, Kam-Chau, 2016. "Likelihood relations and stochastic preferences," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 28-35.
    15. Christopher Turansick, 2023. "An Alternative Approach for Nonparametric Analysis of Random Utility Models," Papers 2303.14249, arXiv.org, revised May 2024.
    16. Indraneel Dasgupta & Prasanta Pattanaik, 2007. "‘Regular’ choice and the weak axiom of stochastic revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 35-50, April.
    17. repec:zbw:rwirep:0070 is not listed on IDEAS
    18. Castillo, Geoffrey, 2020. "The attraction effect and its explanations," Games and Economic Behavior, Elsevier, vol. 119(C), pages 123-147.
    19. Shasikanta Nandeibam, 2009. "On probabilistic rationalizability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 425-437, March.
    20. Kawaguchi, Kohei, 2017. "Testing rationality without restricting heterogeneity," Journal of Econometrics, Elsevier, vol. 197(1), pages 153-171.
    21. Jens Hougaard & Tue Tjur & Lars Østerdal, 2012. "On the meaningfulness of testing preference axioms in stated preference discrete choice experiments," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 13(4), pages 409-417, August.

    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:spr:fuzodm:v:17:y:2018:i:3:d:10.1007_s10700-017-9272-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.