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

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  • 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
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    References listed on IDEAS

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    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Tavares, L. Valadares, 2012. "An acyclic outranking model to support group decision making within organizations," Omega, Elsevier, vol. 40(6), pages 782-790.
    20. 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.
    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.
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