Abstract
Intuitionistic hesitant fuzzy set (IHFS) provides a valid mean for dealing with the uncertainty of complex problems. Information measures on IHFS can measure the uncertain information, so that we shall introduce a method to construct a class of distance measures for IHFS in this paper. For constructing more objective distance measures to reflect the actual situation, we consider the information content and information clarity of IHFS simultaneously and utilize different functions to adjust their contribution. Its superiority is evidenced by an example of pattern recognition that the proposed distance measure improves numerically results obtained with existing distance measures. In particular, we investigate the connection between distance measure, similarity measure, and entropy measure of IHFS, and prove that they can be constructed mutually under this axiomatic framework. On this basis, we apply the proposed entropy measure to determine criteria weights in multi-criteria decision-making problems and design an extended intuitionistic hesitant fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) method, which effectiveness is presented by a practical application.
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Acknowledgements
The authors would like to thank the anonymous referees for helping them refine the ideas presented in this paper and improve the clarity of the presentation. This paper was supported by National Science Foundation of China (Grant nos. 11671244, 12071271).
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Communicated by Regivan Hugo Nunes Santiago.
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Chen, X., Suo, C. & Li, Y. Distance measures on intuitionistic hesitant fuzzy set and its application in decision-making. Comp. Appl. Math. 40, 84 (2021). https://doi.org/10.1007/s40314-021-01478-7
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DOI: https://doi.org/10.1007/s40314-021-01478-7
Keywords
- Intuitionistic hesitant fuzzy set
- Information measures
- Distance measure
- Multi-criteria decision-making
- TOPSIS method