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An approach to hesitant fuzzy multi-stage multi-criterion decision making

Huchang Liao (Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai, China)
Zeshui Xu (Business School, Sichuan University, Chengdu, China)
Jiuping Xu (Business School, Sichuan University, Chengdu, China)


ISSN: 0368-492X

Article publication date: 3 November 2014




The purpose of this paper is to develop some weight determining methods for hesitant fuzzy multi-criterion decision making (MCDM) in which the preference information on attributes is collected over different periods.


Based on the proposed weight determining methods and dynamic hesitant fuzzy aggregation operators, an approach is developed to solve the hesitant fuzzy multi-stage multi-attribute decision-making problem where all the preference information of attributes over different periods is represented in hesitant fuzzy values.


In order to determine the weights associated with dynamic hesitant fuzzy operators, the authors propose the improved maximum entropy method and the minimum average deviation method.

Research limitations/implications

This paper does not consider the multi-stage multi-criteria group decision-making problem.

Practical implications

An example concerning the evaluation of rangelands is given to illustrate the validation and efficiency of the proposed approach. It should be stated that the proposed approach can also be implemented into other multi-stage MCDM problems.


The concept of hesitant fuzzy variable (HFV) is defined. Some operational laws and properties of the HFVs are given. Moreover, to fuse the multi-stage hesitant fuzzy information, the aggregation operators of hesitant fuzzy sets are extended to that of the HFVs.



The authors would like to thank the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper. The work was supported in part by the National Natural Science Foundation of China (No. 61273209), the Excellent PhD thesis Foundation of Shanghai Jiao Tong University (No. 20131216), and the Scholarship from China Scholarship Council (No. 201306230047).


Liao, H., Xu, Z. and Xu, J. (2014), "An approach to hesitant fuzzy multi-stage multi-criterion decision making", Kybernetes, Vol. 43 No. 9/10, pp. 1447-1468.



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