IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v24y2015i5d10.1007_s10726-014-9411-9.html
   My bibliography  Save this article

Lattice Order Group Decision Making with Interval Probability Based on Prospect Theory

Author

Listed:
  • Chun-xiang Guo

    (Business School of Sichuan University)

  • Ying Peng

    (Architecture and Environment School of Sichuan University)

Abstract

A random lattice order decision analysis method is proposed based on an interval probability distribution preference vector by way of entropy theory, focusing on a decision preference system in which preference relation probability is described by interval values and the decision maker’s behavior is also considered. The preference characterization of decision makers is extended from four varieties of relations to seven varieties of preference relations. In addition to the concept, property, and operation rules of interval probability, the concept of interval-valued distribution preference vectors and the relative entropy on the lattice-ordered preference system are given. Then, the interval probability can be more precisely determined, and the weighting interval probability is transformed into the interval probability weight. The ER nonlinear optimization model based on preference entropy is established, individual preferences are aggregated by applying the priority rule and the intersection rule, and the specific steps of decision making are given. Finally, the feasibility and effectiveness of the approach proposed in this paper are illustrated with a numerical example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:24:y:2015:i:5:d:10.1007_s10726-014-9411-9
    DOI: 10.1007/s10726-014-9411-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-014-9411-9
    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/s10726-014-9411-9?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. Han Bleichrodt & Ulrich Schmidt & Horst Zank, 2009. "Additive Utility in Prospect Theory," Management Science, INFORMS, vol. 55(5), pages 863-873, May.
    2. Ulrich Schmidt & Horst Zank, 2008. "Risk Aversion in Cumulative Prospect Theory," Management Science, INFORMS, vol. 54(1), pages 208-216, January.
    3. Guo, Peijun & Tanaka, Hideo, 2010. "Decision making with interval probabilities," European Journal of Operational Research, Elsevier, vol. 203(2), pages 444-454, June.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    6. Jabeur, Khaled & Martel, Jean-Marc, 2007. "A collective choice method based on individual preferences relational systems (p.r.s.)," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1549-1565, March.
    7. 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.
    8. Khaled Jabeur & Jean-Marc Martel, 2010. "An Agreement Index with Respect to a Consensus Preorder," Group Decision and Negotiation, Springer, vol. 19(6), pages 571-590, November.
    9. Frini, Anissa & Guitouni, Adel & Martel, Jean-Marc, 2012. "A general decomposition approach for multi-criteria decision trees," European Journal of Operational Research, Elsevier, vol. 220(2), pages 452-460.
    10. Saaty, Thomas L., 1990. "How to make a decision: The analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 48(1), pages 9-26, September.
    11. Rebai, Abdelwaheb & Aouni, Belaid & Martel, Jean-Marc, 2006. "A multi-attribute method for choosing among potential alternatives with ordinal evaluation," European Journal of Operational Research, Elsevier, vol. 174(1), pages 360-373, October.
    12. Amor, Sarah Ben & Jabeur, Khaled & Martel, Jean-Marc, 2007. "Multiple criteria aggregation procedure for mixed evaluations," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1506-1515, September.
    13. Cook, Wade D., 2006. "Distance-based and ad hoc consensus models in ordinal preference ranking," European Journal of Operational Research, Elsevier, vol. 172(2), pages 369-385, July.
    14. Gonzalez-Pachon, Jacinto & Romero, Carlos, 2004. "A method for dealing with inconsistencies in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 158(2), pages 351-361, October.
    15. Tavares, L. Valadares, 2012. "An acyclic outranking model to support group decision making within organizations," Omega, Elsevier, vol. 40(6), pages 782-790.
    16. Ma, Li-Ching, 2010. "Visualizing preferences on spheres for group decisions based on multiplicative preference relations," European Journal of Operational Research, Elsevier, vol. 203(1), pages 176-184, May.
    17. Podinovski, Vladislav V., 2012. "Sensitivity analysis for choice problems with partial preference relations," European Journal of Operational Research, Elsevier, vol. 221(1), pages 198-204.
    18. Khaled Jabeur & Jean-Marc Martel & Slim Ben Khélifa, 2004. "A Distance-Based Collective Preorder Integrating the Relative Importance of the Group's Members," Group Decision and Negotiation, Springer, vol. 13(4), pages 327-349, July.
    19. Jabeur, Khaled & Martel, Jean-Marc, 2007. "An ordinal sorting method for group decision-making," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1272-1289, August.
    20. Manel Baucells & Antonio Villasís, 2010. "Stability of risk preferences and the reflection effect of prospect theory," Theory and Decision, Springer, vol. 68(1), pages 193-211, February.
    21. González-Pachón, Jacinto & Romero, Carlos, 2011. "The design of socially optimal decisions in a consensus scenario," Omega, Elsevier, vol. 39(2), pages 179-185, April.
    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. Stefan Zeisberger & Dennis Vrecko & Thomas Langer, 2012. "Measuring the time stability of Prospect Theory preferences," Theory and Decision, Springer, vol. 72(3), pages 359-386, March.
    2. Xin Yao & Hai-xiang Guo & Jian Zhu & Yong Shi, 2022. "Dynamic selection of emergency plans of geological disaster based on case-based reasoning and prospect theory," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 110(3), pages 2249-2275, February.
    3. Ben Amor, Sarah & Martel, Jean-Marc, 2014. "A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1165-1169.
    4. Botzen, W.J.W. & van den Bergh, J.C.J.M., 2012. "Risk attitudes to low-probability climate change risks: WTP for flood insurance," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 151-166.
    5. Philip Bromiley, 2009. "A Prospect Theory Model of Resource Allocation," Decision Analysis, INFORMS, vol. 6(3), pages 124-138, September.
    6. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    7. Katarzyna Werner & Horst Zank, 2012. "Foundations for Prospect Theory Through Probability Midpoint Consistency," Economics Discussion Paper Series 1210, Economics, The University of Manchester.
    8. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    9. Lei Wang & Qing Liu & Tongle Yin, 2018. "Decision-making of investment in navigation safety improving schemes with application of cumulative prospect theory," Journal of Risk and Reliability, , vol. 232(6), pages 710-724, December.
    10. Glimcher, Paul W. & Tymula, Agnieszka A., 2023. "Expected subjective value theory (ESVT): A representation of decision under risk and certainty," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 110-128.
    11. Attema, Arthur E. & Brouwer, Werner B.F. & l’Haridon, Olivier & Pinto, Jose Luis, 2016. "An elicitation of utility for quality of life under prospect theory," Journal of Health Economics, Elsevier, vol. 48(C), pages 121-134.
    12. Dierkes, Maik & Erner, Carsten & Zeisberger, Stefan, 2010. "Investment horizon and the attractiveness of investment strategies: A behavioral approach," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 1032-1046, May.
    13. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    14. Charles-Cadogan, G., 2016. "Expected utility theory and inner and outer measures of loss aversion," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 10-20.
    15. Schmidt, Ulrich & Zank, Horst, 2010. "Endogenizing prospect theory's reference point," Kiel Working Papers 1611, Kiel Institute for the World Economy (IfW Kiel).
    16. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    17. Zhiying Wang & Xiaodi Liu & Shitao Zhang, 2019. "A New Decision Method for Public Opinion Crisis with the Intervention of Risk Perception of the Public," Complexity, Hindawi, vol. 2019, pages 1-14, July.
    18. Adam Oliver, 2018. "Your money and your life: Risk attitudes over gains and losses," Journal of Risk and Uncertainty, Springer, vol. 57(1), pages 29-50, August.
    19. Ferdinand M. Vieider & Peter Martinsson & Pham Khanh Nam & Nghi Truong, 2019. "Risk preferences and development revisited," Theory and Decision, Springer, vol. 86(1), pages 1-21, February.
    20. Lin, Chen & Xiao, Hui & Peng, Rui & Xiang, Yisha, 2021. "Optimal defense-attack strategies between M defenders and N attackers: A method based on cumulative prospect theory," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

    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:grdene:v:24:y:2015:i:5:d:10.1007_s10726-014-9411-9. 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.