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Hesitant Fuzzy Linguistic Archimedean Aggregation Operators in Decision Making with the Dempster–Shafer Belief Structure

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Abstract

We propose a novel method for hesitant fuzzy linguistic decision making by utilizing Dempster–Shafer (D–S) theory of evidence. First, we propose some novel operations of hesitant fuzzy linguistic term sets (HFLTSs) on the basis of closed operations on linguistic 2-tuples and distribution linguistic average aggregation (DLAA) operators. These novel operations not only avoid information loss and operational results exceeding the boundary of linguistic term sets, but also make the aggregation results interpretable. Then, we define the hesitant fuzzy linguistic Archimedean weighted arithmetic mean (HFLAWAM) and hesitant fuzzy linguistic Archimedean weighted geometric mean (HFLAWGM) operators of HFLTSs. These two proposed operators are able to overcome the shortcomings of the existing approaches to multicriteria decision making (MCDM) with HFLTSs. Then, to take into account the novel operations of HFLTSs and the MCDM under uncertainty, we propose the belief structure-HFLAWAM (BS-HFLAWAM) and belief structure-HFLAWGM (BS-HFLAWGM) operators of HFLTSs. After that, we create an approach to handle the hesitant fuzzy linguistic MCDM problems in light of proposed operators. Finally, we apply the created approach to a MCDM problem regarding political management of a country.

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Acknowledgements

This article was funded by Special Funds of Taishan Scholars Project in Shandong Province (No. ts201511045) and National Natural Science Foundation of China (Nos. 71771140, 61603010, 61773029, 71471172, 61273230, 61603011).

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Authors and Affiliations

  1. School of Economics and Management, Beijing University of Technology, Beijing, 100124, China

    Chao Liu & Guolin Tang

  2. Research Base of Beijing Modern Manufacturing Development, Beijing, 100124, China

    Chao Liu & Guolin Tang

  3. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu

  4. School of Mathematics and Computer Science, Dickinson College, Carlisle, PA, 17013, USA

    Chenqi Liu

Authors
  1. Chao Liu
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  2. Guolin Tang
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  3. Peide Liu
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  4. Chenqi Liu
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Correspondence to Guolin Tang.

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Liu, C., Tang, G., Liu, P. et al. Hesitant Fuzzy Linguistic Archimedean Aggregation Operators in Decision Making with the Dempster–Shafer Belief Structure. Int. J. Fuzzy Syst. 21, 1330–1348 (2019). https://doi.org/10.1007/s40815-019-00660-8

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  • DOI: https://doi.org/10.1007/s40815-019-00660-8

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