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Grey Relational Analysis Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Geometric Bonferroni Mean

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Abstract

In practical decision-making problems, probabilistic linguistic term sets (PLTSs) are a very useful and flexible way to represent the qualitative judgments of experts. The PLTSs also have strong ability to express the information vagueness and uncertainty in the real-world applications. Considering the interrelationship among the input arguments of PLTSs, we extend the geometric Bonferroni mean to the probabilistic linguistic environment and design an approach for the application of multi-criteria group decision-making with PLTSs. First, we develop the probabilistic linguistic geometric Bonferroni mean and the weighted probabilistic linguistic geometric Bonferroni mean (WPLGBM) operators. The properties of these aggregation operators are investigated. Second, we utilize the WPLGBM operators to fuse the information in the probabilistic linguistic multi-criteria group decision-making (PLMCGDM) problem, which can obtain much more information in the process of group decision-making. By introducing the grey relational analysis method, we present its extension and further design a new approach for the PLMCGDM. Finally, an example is given to elaborate our proposed algorithm and successfully validate its performance.

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Acknowledgements

This work is partially supported by the National Science Foundation of China (Nos. 71401026, 71432003, 71571148), the National Social Science Foundation of China (No. 14BGL152), the Fundamental Research Funds for the Central Universities of China (No. ZYGX2014J100), the Social Science Planning Project of the Sichuan Province (No. SC15C009), and the Major Project of the Sichuan Research Center of Electronic Commerce and Modern Logistics (No. DSWL16-3).

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Authors and Affiliations

  1. School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Decui Liang & Agbodah Kobina

  2. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Wei Quan

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  1. Decui Liang
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  2. Agbodah Kobina
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  3. Wei Quan
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Correspondence to Decui Liang.

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Liang, D., Kobina, A. & Quan, W. Grey Relational Analysis Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Geometric Bonferroni Mean. Int. J. Fuzzy Syst. 20, 2234–2244 (2018). https://doi.org/10.1007/s40815-017-0374-2

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  • DOI: https://doi.org/10.1007/s40815-017-0374-2

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