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Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers

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Abstract

A hesitant fuzzy linguistic set is an extension of both a linguistic term set and a hesitant fuzzy set. It combines a quantitative evaluation with a qualitative evaluation, which can describe the real preferences of decision makers and reflect their uncertainty, hesitancy and inconsistency. The focus of this paper is those multi-criteria decision-making (MCDM) problems in which the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). Having reviewed the relevant literature, the Hausdorff distance for HFLNs is provided and some linguistic scale functions are applied. Subsequently, two hesitant fuzzy linguistic MCDM methods are proposed, which are based on the proposed distance measure and the TOPSIS and TODIM methods. The first of these MCDM methods is based on complete rationality, whilst the second is based on bounded rationality. Finally, an illustrative example is provided to verify the proposed methods, which are then compared to the existing approaches.

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Acknowledgments

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 71271218, 71431006 and 71221061).

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Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, China

    Jian-qiang Wang, Jia-ting Wu, Jing Wang, Hong-yu Zhang & Xiao-hong Chen

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  1. Jian-qiang Wang
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  2. Jia-ting Wu
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  3. Jing Wang
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  4. Hong-yu Zhang
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  5. Xiao-hong Chen
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Correspondence to Jian-qiang Wang.

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Communicated by V. Loia.

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Wang, Jq., Wu, Jt., Wang, J. et al. Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers. Soft Comput 20, 1621–1633 (2016). https://doi.org/10.1007/s00500-015-1609-5

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