Soft Computing

, Volume 21, Issue 12, pp 3439–3459 | Cite as

Hesitant fuzzy multi-attribute decision-making based on the minimum deviation method

  • Hua Zhao
  • Zeshui XuEmail author
  • Hai Wang
  • Shousheng Liu
Methodologies and Application


As a powerful and efficient tool in expressing the indeterminate and fuzzy information, the hesitant fuzzy set (HFS) has shown its increasing importance. It was first proposed by Torra and Narukawa, permitting the membership degree of an element to a set of several possible values. In this paper, based on the idea of minimum deviation between the subjective and the objective preferences, we first develop two methods to determine the attribute weights under the hesitant fuzzy environment. To do so, we present the concept of hesitant fuzzy expected value and then establish several optimization models to gain the attribute weights. After that, we use the information aggregation techniques to integrate the hesitant fuzzy attribute values or their expected values, and then sort the alternatives by the overall values. Moreover, we generalize these two methods to interval-valued HFSs, and a numerical example is utilized to show the detailed implementation procedure and effectiveness of our methods in solving multi-attribute decision-making problems with hesitant fuzzy or interval-valued hesitant fuzzy information.


Hesitant fuzzy set Multi-attribute decision-making  Minimum deviation Weight 



The work was supported by the National Natural Science Foundation of China (No. 61273209) and the Central University Basic Scientific Research Business Expenses Project (No. skgt201501).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of SciencesPLA University of Science and TechnologyNanjingChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.School of Economics and ManagementSoutheast UniversityNanjingChina

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