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Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment

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  • Zeshui Xu

    (Sichuan University)

  • Wei Zhou

    (Yunnan University of Finance and Economics)

Abstract

As a generalized fuzzy number, the hesitant fuzzy element (HFE) has been receiving increased attention and has recently become a popular topic. However, we find that the occurring probabilities of the possible values in the HFE are equal, which is obviously impractical. Consequently, in this paper, we propose a hesitant fuzzy number with probabilities, called the hesitant probabilistic fuzzy number, and construct its score function, deviation function, comparison laws, and its basic operations. It is well known that in the context of a group of decision makers (DMs), one of the basic approaches to built consensus is to aggregate individual evaluations or individual priorities. Thus, to use the hesitant fuzzy numbers for consensus building with a group of DMs, we further propose a method called maximizing score deviation method to obtain the DMs’ weights under the HPFE environment, based on which two extended and four new ordered weighted operators are provided to fuse the HPFE information and build the consensus of the DMs. We also analyze the differences among these ordered weighted operators and provide their application scopes. Finally, a practical case is provided to demonstrate consensus building with a group of DMs under the HPFE environment using the proposed approaches.

Suggested Citation

  • Zeshui Xu & Wei Zhou, 2017. "Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment," Fuzzy Optimization and Decision Making, Springer, vol. 16(4), pages 481-503, December.
    • Handle: RePEc:spr:fuzodm:v:16:y:2017:i:4:d:10.1007_s10700-016-9257-5
    DOI: 10.1007/s10700-016-9257-5
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    References listed on IDEAS

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    1. Zhou, Wei & Xu, Zeshui, 2016. "Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites," European Journal of Operational Research, Elsevier, vol. 254(2), pages 610-621.
    2. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Feng, Bo, 2010. "The OWA-based consensus operator under linguistic representation models using position indexes," European Journal of Operational Research, Elsevier, vol. 203(2), pages 455-463, June.
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    4. Ramanathan, R. & Ganesh, L. S., 1994. "Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages," European Journal of Operational Research, Elsevier, vol. 79(2), pages 249-265, December.
    5. Alfredo Altuzarra & José María Moreno-Jiménez & Manuel Salvador, 2010. "Consensus Building in AHP-Group Decision Making: A Bayesian Approach," Operations Research, INFORMS, vol. 58(6), pages 1755-1773, December.
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    Cited by:

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