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Fuzzy Group Decision Making for Multiobjective Problems: Tradeoff between Consensus and Robustness

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Listed:
  • Jian Xiong
  • Xu Tan
  • Ke-wei Yang
  • Ying-wu Chen

Abstract

Many decision making problems involve multiple decision makers and conflicting objectives. This paper refers to this kind of problems as group decision making for multiobjective problems (GDM‐MOP). The task of GDM‐MOP is to select final solution(s) from a set of nondominated solutions according to the decision makers′ preferences. However, it is common that the preference could be imprecise. We study the GDM‐MOP where preferences are expressed by fuzzy reference points, called as fuzzy GDMMOP (FGDM‐MOP). This paper provides a decision support model to simultaneously consider two measures for FGDM‐MOP: consensus measure and robustness measure. The former is used to reflect the acceptable degree of a solution by the decision making group, while the latter indicates a solution′s ability to cope with any change on preferences. A multiobjective evolutionary approach is presented to solve the problem. Finally, a modified benchmark function is studied to illustrate the proposed approach.

Suggested Citation

  • Jian Xiong & Xu Tan & Ke-wei Yang & Ying-wu Chen, 2013. "Fuzzy Group Decision Making for Multiobjective Problems: Tradeoff between Consensus and Robustness," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:657978
    DOI: 10.1155/2013/657978
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    References listed on IDEAS

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    1. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    2. Selcen (Pamuk) Phelps & Murat Köksalan, 2003. "An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization," Management Science, INFORMS, vol. 49(12), pages 1726-1738, December.
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    1. Juuso Pajasmaa & Kaisa Miettinen & Johanna Silvennoinen, 2025. "Group Decision Making in Multiobjective Optimization: A Systematic Literature Review," Group Decision and Negotiation, Springer, vol. 34(2), pages 329-371, April.
    2. Wei Xiong, 2014. "Games under Ambiguous Payoffs and Optimistic Attitudes," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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