Soft Computing

, Volume 22, Issue 16, pp 5513–5524 | Cite as

Multiple-attribute decision-making method based on hesitant fuzzy linguistic Muirhead mean aggregation operators

  • Peide LiuEmail author
  • Ying Li
  • Maocong Zhang
  • Li Zhang
  • Juan Zhao


The hesitant fuzzy linguistic (HFL) variable can handle the uncertainty very well, and Muirhead mean (MM) operator can consider correlations among any amount of inputs by an alterable parameter, which is a generalization of some existing operators by changing the parameter values. However, the traditional MM is only suitable for crisp numbers. In this article, we enlarge the scope of the MM operator to the HFL circumstance, and two new aggregation operators are proposed, including the HFL Muirhead mean operator and the weighted HFL Muirhead mean (WHFLMM) operator. Simultaneously, we discuss some worthy characters and some special cases concerning diverse parameter values of these operators. Moreover, a multiple-attribute decision-making method under the HFL environment is developed based on the WHFLMM operator. Lastly, a numerical example is applied to explain the feasibility of the proposed method.


HFL MM operator MADM 



This paper is supported by the National Natural Science Foundation of China (Nos. 71771140, 71471172, and 71271124), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), Shandong Provincial Social Science Planning Project (Nos. 16CGLJ31 and 16CKJJ27), the Natural Science Foundation of Shandong Province (No. ZR2017MG007), the Teaching Reform Research Project of Undergraduate Colleges and Universities in Shandong Province (No. 2015Z057), and Key research and development program of Shandong Province (No. 2016GNC110016). The authors also would like to express appreciation to the anonymous reviewers and editors for their very helpful comments that improved the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

Human and animals rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Management Science and EngineeringShandong University of Finance and EconomicsJinanChina
  2. 2.Department of Development Planning and Discipline ConstructionShandong Normal UniversityJinanChina
  3. 3.School of Economics and ManagementShandong Yingcai UniversityJinanChina

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