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Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR

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Abstract

Linguistic hesitant intuitionistic fuzzy set, which allows an element having several linguistic evaluation values and each linguistic argument having several intuitionistic fuzzy memberships, is a power tool to model uncertain information existing in multiple attribute decision-making problems. In this paper, we propose new methods by using TOPSIS and VIKOR for multiple attribute decision-making problems, in which evaluation values are in the form of linguistic hesitant intuitionistic fuzzy elements. Different situations of attribute weight information are considered. If attribute weights are partly known, a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the linguistic hesitant intuitionistic fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. A numerical example is presented to illustrate feasibility and practical advantages of the proposed method. We compare the alternatives’ rankings derived from the linguistic hesitant intuitionistic fuzzy TOPSIS method with those derived from the hesitant fuzzy linguistic TOPSIS and the hesitant intuitionistic fuzzy TOPSIS approach to further illustrate their advantages.

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Acknowledgments

The authors would like to express appreciation to the anonymous reviewers for their very helpful comments on improving the paper. This work is partly supported by National Natural Science Foundation of China (Nos. 11401457, 61403298), Postdoctoral Science Foundation of China (2015M582624), Shaanxi Province Natural Science Fund of China (Nos. 2014JQ1019, 2014JM1010).

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Authors and Affiliations

  1. Xi’an University of Architecture and Technology, Xi’an, 710055, People’s Republic of China

    Wei Yang, Yongfeng Pang, Jiarong Shi & Chengjun Wang

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  1. Wei Yang
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  2. Yongfeng Pang
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  3. Jiarong Shi
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  4. Chengjun Wang
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Correspondence to Wei Yang.

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Yang, W., Pang, Y., Shi, J. et al. Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR. Neural Comput & Applic 29, 613–626 (2018). https://doi.org/10.1007/s00521-016-2526-y

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