Abstract
Hesitant fuzzy soft set (HFSS) can be considered an effective parameterized tool for dealing with vagueness and uncertainty. Considering that the classical HFSS does not involve the importance of all of the possible membership degrees of each element, in this paper, a new concept of weighted hesitant fuzzy soft set (WHFSS) is proposed by assigning a weight vector to all of the possible membership degrees of each element. First, we introduce the definition, basic operations, and score function of WHFSS. Then, some kinds of weighted hesitant fuzzy soft aggregation operators are proposed to incorporate two important weighting factors in terms of membership values and parameters. Furthermore, based on the proposed operators, we develop a novel approach for multi-criteria group decision making (MCGDM) under a weighted hesitant fuzzy soft environment. It can flexibly handle HFSS-based MCGDM problems with complete or incomplete information as input in two cases (experts’ weights unknown or known). Meanwhile, two corresponding algorithms to determine the membership weights are developed, respectively. The newly proposed method can guarantee assessment consistency when each expert may provide more than one evaluation value in final group decision-making, especially in the case of experts’ weights being unknown. Compared with some existing approaches in HFSS, the presented method utilizing a WHFSS-based decision model builds on the existing data without adding any extra elements to represent the unknown possible membership values. It is more objective and reasonable to measure the consistency of assessment between decision-makers. Finally, the effectiveness and practicality of our proposed approach are demonstrated by some illustrative examples.
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28 June 2023
A Correction to this paper has been published: https://doi.org/10.1007/s41066-023-00394-x
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Acknowledgements
The authors are thankful to the editor and anonymous reviewers for their constructive comments and suggestions that helped us improving the paper significantly. This work was supported by the National Natural Science Foundation of China (No.11961045) and Scientific Research Fund of Jiangxi Provincial Education Department (No.150196).
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Wen, X. Weighted hesitant fuzzy soft set and its application in group decision making. Granul. Comput. 8, 1583–1605 (2023). https://doi.org/10.1007/s41066-023-00387-w
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DOI: https://doi.org/10.1007/s41066-023-00387-w