Soft Computing

, Volume 21, Issue 21, pp 6253–6267 | Cite as

A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model

  • Hai-Long Yang
  • Chun-Ling Zhang
  • Zhi-Lian Guo
  • Yan-Ling Liu
  • Xiuwu Liao


Smarandache initiated neutrosophic sets (NSs) as a tool for handling undetermined information. Wang et al. proposed single valued neutrosophic sets (SVNSs) that is an especial NSs and can be used expediently to deal with real-world problems. In this paper, we propose single valued neutrosophic rough sets by combining single valued neutrosophic sets and rough sets. We study the hybrid model by constructive and axiomatic approaches. Firstly, by using the constructive approach, we propose the lower/upper single valued neutrosophic approximation operators and illustrate the connections between special single valued neutrosophic relations (SVNRs) and the lower/upper single valued neutrosophic approximation operators. Then, by using the axiomatic approach, we discuss the operator-oriented axiomatic characterizations of single valued neutrosophic rough sets. We obtain that different axiom sets of the lower/upper single valued neutrosophic set-theoretic operators guarantee the existence of different classes of SVNRs which produce the same operators. Finally, we introduce single valued neutrosophic rough sets on two-universes and an algorithm of decision making based on single valued neutrosophic rough sets on two-universes, and use an illustrative example to demonstrate the application of the proposed model.


Neutrosophic sets Single valued neutrosophic sets Single valued neutrosophic rough sets Constructive approaches Axiomatic approaches 



The authors would wish to express their sincere gratitude to the anonymous referees and Associate Editor Prof. Tzung-Pei Hong for their valuable comments and helpful suggestions. The first author acknowledges the support of National Natural Science Foundation of China (No. 61473181) and China Postdoctoral Science Foundation funded project (No. 2013M532063); the third author acknowledges the support of National Natural Science Foundation of China (No. 11526163), and the last author acknowledges the support of National Natural Science Foundation of China (No. 91546119).

Compliance with ethical standards

Conflict of interest

Authors declare that they have no conflict of interest.

Ethical approval

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 Berlin Heidelberg 2016

Authors and Affiliations

  • Hai-Long Yang
    • 1
    • 2
  • Chun-Ling Zhang
    • 1
  • Zhi-Lian Guo
    • 3
  • Yan-Ling Liu
    • 1
  • Xiuwu Liao
    • 2
  1. 1.College of Mathematics and Information ScienceShaanxi Normal UniversityXi’anPeople’s Republic of China
  2. 2.School of ManagementXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  3. 3.College of EconomicsNorthwest University of Political Science and LawXi’anPeople’s Republic of China

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