Neural Computing and Applications

, Volume 29, Issue 7, pp 613–626 | Cite as

Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR

  • Wei Yang
  • Yongfeng Pang
  • Jiarong Shi
  • Chengjun Wang
Original Article


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.


Hesitant fuzzy set Linguistic hesitant intuitionistic fuzzy set TOPSIS VIKOR Multiple attribute decision making 



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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Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Wei Yang
    • 1
  • Yongfeng Pang
    • 1
  • Jiarong Shi
    • 1
  • Chengjun Wang
    • 1
  1. 1.Xi’an University of Architecture and TechnologyXi’anPeople’s Republic of China

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