Cognitive Computation

, Volume 10, Issue 5, pp 752–768 | Cite as

Outranking Decision-Making Method with Z-Number Cognitive Information

  • Hong-gang Peng
  • Jian-qiang Wang


The Z-number provides an adequate and reliable description of cognitive information. The nature of Z-numbers is complex, however, and important issues in Z-number computation remain to be addressed. This study focuses on developing a computationally simple method with Z-numbers to address multicriteria decision-making (MCDM) problems. Processing Z-numbers requires the direct computation of fuzzy and probabilistic uncertainties. We used an effective method to analyze the Z-number construct. Next, we proposed some outranking relations of Z-numbers and defined the dominance degree of discrete Z-numbers. Also, after analyzing the characteristics of elimination and choice translating reality III (ELECTRE III) and qualitative flexible multiple criteria method (QUALIFLEX), we developed an improved outranking method. To demonstrate this method, we provided an illustrative example concerning job-satisfaction evaluation. We further verified the validity of the method by a criteria test and comparative analysis. The results demonstrate that the method can be successfully applied to real-world decision-making problems, and it can identify more reasonable outcomes than previous methods. This study overcomes the high computational complexity in existing Z-number computation frameworks by exploring the pairwise comparison of Z-numbers. The method inherits the merits of the classical outranking method and considers the non-compensability of criteria. Therefore, it has remarkable potential to address practical decision-making problems involving Z-information.


Multicriteria decision-making Z-number Outranking relation ELECTRE III QUALIFLEX 



The authors are very grateful to the anonymous reviewers and the editor for their insightful and constructive comments and suggestions that have led to an improved version of this paper. And, this work was supported by the National Natural Science Foundation of China (No. 71571193).

Compliance with Ethical Standards

Conflict of Interest

Hong-gang Peng and Jian-qiang Wang declare that they have no conflict of interest.

Informed Consent

Informed consent was not required as no humans or animals were involved.

Human and Animal Rights

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


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

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

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