International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1300–1316 | Cite as

Hesitant Uncertain Linguistic Z-Numbers and Their Application in Multi-criteria Group Decision-Making Problems



This paper introduces hesitant uncertain linguistic Z-numbers (HULZNs) based on Z-numbers and linguistic models. HULZNs can serve as a reliable tool to depict complex and uncertain decision-making information and reflect the hesitancy of DMs. This paper focuses on the development of an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is incompletely known. Handling qualitative information requires the effective support of quantitative tools, after which the linguistic scale function is employed to deal with linguistic information. First, the operations and distance of HULZNs are defined. Then, two power aggregation operators for HULZNs are proposed. Subsequently, a new MCGDM approach is developed by incorporating the power aggregation operators and the VIKOR model. Finally, an illustrative example of ERP system selection is provided for demonstration, and the feasibility and validity of the proposed method are further verified by sensitivity analysis and comparison with an existing method.


Multi-criteria group decision-making Hesitant uncertain linguistic Z-numbers Linguistic scale function Power aggregation operators VIKOR method 



The authors thank the editors and anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 71571193 and 71271218).


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaPeople’s Republic of China

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