Skip to main content
SpringerLink
Log in

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

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MathSciNet  MATH  Google Scholar 

  • Broumi S, Smarandache F (2014) Rough neutrosophic sets. Ital J Pure Appl Math 32:493–502

    MathSciNet  MATH  Google Scholar 

  • Broumi S, Smarandache F, Single valued neutrosophic information systems based on rough set theory, https://www.researchgate.net/publication/280742564

  • Bonikowski Z, Bryniarski E, Wybraniec-Skardowska U (1998) Extensions and intentions in the rough set theory. Inf Sci 107:149–167

    Article  MathSciNet  MATH  Google Scholar 

  • Cornelis C, Cock MD, Kerre EE (2003) Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Syst Appl 20:260–270

    Article  Google Scholar 

  • Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191–209

    Article  MATH  Google Scholar 

  • Guo Y, Cheng HD (2009) A new neutrosophic approach to image segmentation. Pattern Recogn 42:587–595

    Article  MATH  Google Scholar 

  • Guo Y, Sengur A (2015) NCM: neutrosophic c-means clustering algorithm. Pattern Recogn 48(8):2710–2724

    Article  Google Scholar 

  • Majumdar P, Samant SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26(3):1245–1252

    MathSciNet  MATH  Google Scholar 

  • Mi JS, Zhang WX (2004) An axiomatic characterization of a fuzzy generalized of rough sets. Inf Sci 160:235–249

    Article  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11:341–356

    Article  MATH  Google Scholar 

  • Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic, Dordrecht

    Book  MATH  Google Scholar 

  • Pei DW (2005) A generalized model of fuzzy rough sets. Int J Gen Syst 34:603–613

    Article  MathSciNet  MATH  Google Scholar 

  • Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346

    Article  Google Scholar 

  • Rivieccio U (2008) Neutrosophic logics: prospects and problems. Fuzzy Sets Syst 159:1860–1868

    Article  MathSciNet  MATH  Google Scholar 

  • Salama AA, Broumi S (2014) Roughness of neutrosophic sets. Elixir Appl Math 74:26833–26837

    Google Scholar 

  • Şahin R, Küçük A (2015) Subsethood measure for single valued neutrosophic sets. J Intell Fuzzy Syst 29(2):525–530

    Article  MATH  Google Scholar 

  • Smarandache F (1998) Neutrosophy. Neutrosophic probability, set, and logic. American Research Press, Rehoboth

    MATH  Google Scholar 

  • Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth

    MATH  Google Scholar 

  • Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413

    MATH  Google Scholar 

  • Wu WZ, Mi JS, Zhang WX (2003) Generalized fuzzy rough sets. Inf Sci 151:263–282

    Article  MathSciNet  MATH  Google Scholar 

  • Wu WZ, Xu YH, Shao MW, Wang G (2016) Axiomatic characterizations of \((S, T)\)-fuzzy rough approximation operators. Inf Sci 334–335:17–43

    Google Scholar 

  • Yang XB, Song XN, Qi YS, Yang JY (2014) Constructive and axiomatic approaches to hesitant fuzzy rough set. Soft Comput 18:1067–1077

    Article  MATH  Google Scholar 

  • Yang H-L, Guo Z-L, She YH, Liao XW (2016) On single valued neutrosophic relations. J Intell Fuzzy Syst 30:1045–1056

    Article  MATH  Google Scholar 

  • Yang H-L, Li S-G, Guo Z-L, Ma C-H (2012) Transformation of bipolar fuzzy rough set models. Knowl Based Syst 27:60–68

    Article  Google Scholar 

  • Yang H-L, Li S-G, Wang SY, Wang J (2012) Bipolar fuzzy rough set model on two different universes and its application. Knowl Based Syst 35:94–101

    Article  Google Scholar 

  • Yao YY (2015) The two sides of the theory of rough sets. Knowl Based Syst 80:67–77

    Article  Google Scholar 

  • Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109:21–47

    Article  MathSciNet  MATH  Google Scholar 

  • Yao YY (1998) On generalizing pawlak approximation operators. LNAI 1424:298–307

    MathSciNet  MATH  Google Scholar 

  • Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394

    Article  MathSciNet  MATH  Google Scholar 

  • Ye J (2014) Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making. J Intell Fuzzy Syst 27:2453–2462

    MATH  Google Scholar 

  • Ye J (2014) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466

    MathSciNet  MATH  Google Scholar 

  • Yeung DS, Chen DG, Tsang ECC, Lee JWT, Wang XZ (2005) On the generalization of fuzzy rough sets. IEEE Trans Fuzzy Syst 13:343–361

    Article  Google Scholar 

  • Zhang XH, Zhou B, Li P (2012) A general frame for intuitionistic fuzzy rough sets. Inf Sci 216:34–49

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang ZM (2013) On characterization of generalized interval type-2 fuzzy rough sets. Inf Sci 219:124–150

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang HD, Shu L, Liao SL (2016) On interval-valued hesitant fuzzy rough approximation operators. Soft Comput 20(1):189–209

    Article  MATH  Google Scholar 

  • Zhou L, Wu WZ (2008) On generalized intuitionistic fuzzy approximation operators. Inf Sci 178:2448–2465

    MathSciNet  MATH  Google Scholar 

  • Zhou NL, Hu BQ (2016) Axiomatic approaches to rough approximation operators on complete completely distributive lattices. Inf Sci 348(20):227–242

    Article  MathSciNet  Google Scholar 

  • Zhu W, Wang FY (2007) On three types of covering-based rough sets. IEEE Trans Knowl Data Eng 19(8):1131–1144

    Article  Google Scholar 

Download references

Acknowledgments

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).

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, People’s Republic of China

    Hai-Long Yang, Chun-Ling Zhang & Yan-Ling Liu

  2. School of Management, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Hai-Long Yang & Xiuwu Liao

  3. College of Economics, Northwest University of Political Science and Law, Xi’an, 710063, People’s Republic of China

    Zhi-Lian Guo

Authors
  1. Hai-Long Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chun-Ling Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi-Lian Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yan-Ling Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiuwu Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hai-Long Yang.

Ethics declarations

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.

Additional information

Communicated by A. Di Nola.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, HL., Zhang, CL., Guo, ZL. et al. A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model. Soft Comput 21, 6253–6267 (2017). https://doi.org/10.1007/s00500-016-2356-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-016-2356-y

Keywords

Search

Navigation