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.
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Acknowledgements
The authors would like to thank the editors and the anonymous reviewers for their insightful and constructive suggestions that have led to this improved version of the paper. This work was supported by the National Natural Science Foundation of China (Nos. 71561026, 71571123, and 61273209); and China Postdoctoral Science Foundation (Nos. 2015M570792 and 2016T90864).
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Xu, Z., Zhou, W. Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optim Decis Making 16, 481–503 (2017). https://doi.org/10.1007/s10700-016-9257-5
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DOI: https://doi.org/10.1007/s10700-016-9257-5