Cognitive Computation

, Volume 8, Issue 4, pp 649–669 | Cite as

A Neutrosophic Normal Cloud and Its Application in Decision-Making

  • Hong-yu Zhang
  • Pu Ji
  • Jian-qiang Wang
  • Xiao-hong Chen


In this study, a neutrosophic normal cloud (NNC) and several other related concepts, including a backward cloud generator, two aggregated operators, and an NNC distance measurement, are proposed. Using these concepts, we also construct a multi-criteria group decision-making approach to single-value neutrosophic environments. In the proposed approach, all evaluations provided by decision-makers are aggregated via the backward cloud generator. The resulting NNC reflects the distribution of customer evaluations. An empirical example and a comparative study are also provided in order to illustrate and validate the proposed approach. The results of an empirical case study using data from indicate that the proposed approach could be effectively applied to practical problems.


Neutrosophic normal cloud (NNC) Backward cloud generator Aggregation operator Multi-criteria group decision-making 



This work was supported by the National Natural Science Foundation of China (Nos. 71501192 and 71210003) and the Research Funds for the Scholars of Central South University (No. 2014JSJJ043). The authors also would like to express appreciation to the anonymous reviewers and editors for their helpful comments that improved the paper. Moreover, the authors thank LetPub ( for its linguistic assistance during the preparation of this manuscript.

Compliance with Ethical Standards

Conflict of Interest

Hong-yu Zhang, Pu Ji, Jian-qiang Wang and Xiao-hong Chen declares that they have no conflict of interest.

Informed Consent

All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 (5). Additional informed consent was obtained from all patients for which identifying information is included in this article.

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 Science+Business Media New York 2016

Authors and Affiliations

  • Hong-yu Zhang
    • 1
  • Pu Ji
    • 1
  • Jian-qiang Wang
    • 1
  • Xiao-hong Chen
    • 1
  1. 1.School of BusinessCentral South UniversityChangshaChina

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