Journal
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS
Volume 20, Issue 7, Pages 2234-2244Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40815-017-0374-2
Keywords
Probabilistic linguistic term sets; Geometric Bonferroni mean; Multi-criteria group decision-making; Grey relational analysis
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Funding
- National Science Foundation of China [71401026, 71432003, 71571148]
- National Social Science Foundation of China [14BGL152]
- Fundamental Research Funds for the Central Universities of China [ZYGX2014J100]
- Social Science Planning Project of the Sichuan Province [SC15C009]
- Major Project of the Sichuan Research Center of Electronic Commerce and Modern Logistics [DSWL16-3]
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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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