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A consensus-based approach for multi-criteria decision making with probabilistic hesitant fuzzy information

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Abstract

As a generalized fuzzy number, probabilistic hesitant fuzzy element (PHFE) improves the flexibility for decision makers in expressing hesitant information, and it has been receiving increased attention. This study develops a multi-criteria decision-making (MCDM) approach that considers consensus reaching among decision makers with probabilistic hesitant fuzzy information. To obtain this aim, first, a new approach to derive normalized PHFE (NPHFE) is proposed to overcome the shortcomings in previous studies. Subsequently, a new Euclidean distance and some operations related to PHFEs are developed based on the new proposed NPHFEs. At the same time, the effectiveness and rationality of the new proposed approaches are discussed. Second, a consensus index of group with PHFEs is presented, which based on the proposed Euclidean distance of decision-makers’ evaluation information on all the criteria. Third, if the consensus level of the group does not reach the expect threshold value, an iteration algorithm is designed to improve its consensus level. Moreover, the proof of the convergence of the proposed algorithm is provided to verify its effectiveness, and a MCDM approach based on group consensus is proposed. Finally, the most comprehensive candidate selection problems are provided to demonstrate the effectiveness of the proposed MCDM approach. And a comparative study with other methods is conducted with the same illustrative example.

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Acknowledgements

The authors thank the anonymous reviewers and the editor for their insightful and constructive comments and suggestions that have led to an improved version of this paper. This work was supported by the National Natural Science Foundation of China (No. 61866006), Guangxi innovation-driven development of special funds project (gui ke AA17204091), the Natural Science Foundation of Guangxi (No. AB17292095), the Research Funds for the Guangxi University Xingjian College of Science and Liberal Arts (No. Y2018ZKT01) and Promotion project of Middle-aged and Young Teachers’ Basic Scientific Research Ability in Universities of Guangxi (No. 2019KY0963).

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Authors and Affiliations

  1. School of Logistics Management and Engineering, Nanning Normal University, Nanning, 530001, People’s Republic of China

    Jian Li & Qiongxia Chen

  2. Guangxi University Xingjian College of Science and Liberal Arts, Nanning, 530005, People’s Republic of China

    Li-li Niu & Guang Wu

Authors
  1. Jian Li
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  2. Li-li Niu
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  3. Qiongxia Chen
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  4. Guang Wu
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Correspondence to Qiongxia Chen.

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Authors Jian Li, Li-li Niu, Qiongxia Chen and Guang Wu declare that they have no conflict of interest.

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Communicated by V. Loia.

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Li, J., Niu, Ll., Chen, Q. et al. A consensus-based approach for multi-criteria decision making with probabilistic hesitant fuzzy information. Soft Comput 24, 15577–15594 (2020). https://doi.org/10.1007/s00500-020-04886-9

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