Skip to main content
SpringerLink
Log in

Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Similarity measure is an important tool in pattern recognition and fault diagnosis. This paper proposes two cotangent similarity measures for single-valued neutrosophic sets (SVNSs) based on cotangent function. Then, the weighted cotangent similarity measures are introduced by considering the importance of each element. Moreover, by the comparison between the cotangent similarity measures of SVNSs and existing cosine similarity measure of SVNSs, the developed cotangent similarity measures demonstrate their advantages and rationality and in some cases can overcome some disadvantages of the cosine similarity measure defined in vector space. Finally, the cotangent similarity measures are applied to the fault diagnosis of steam turbine. The proposed fault diagnosis method demonstrates its effectiveness and rationality by the comparative analysis with the cosine similarity measure in the fault diagnosis of steam turbine.

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 20:87–96

    Article  MathSciNet  MATH  Google Scholar 

  • Broumi S, Smarandache F (2013) Several similarity measures of neutrosophic sets. Neutrosophic Sets Syst 1(1):54–62

    Google Scholar 

  • Guo Y, Sengur A, Ye J (2014) A novel image thresholding algorithm based on neutrosophic similarity score. Measurement 58:175–186

    Article  Google Scholar 

  • Liu PD, Chu YC, Li YW, Chen YB (2014) Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making. Int J Fuzzy Syst 16(2):242–255

    Google Scholar 

  • Liu PD, Wang YM (2014) Multiple attribute decision making method based on single valued neutrosophic normalized weighted Bonferroni mean. Neural Comput Appl. doi:10.1007/s00521-014-1688-8

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

    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 Compu 25:336–346

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Tian MY (2013) A new fuzzy similarity based on cotangent function for medical diagnosis. Adv Model Optim 15(2):151–156

    Google Scholar 

  • Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information: application to pattern recognition. Pattern Recogn Lett 28:197–206

    Article  Google Scholar 

  • Wang H, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic: theory and applications in computing. Hexis, Phoenix

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Ye J (2009) Fault diagnosis of turbine based on fuzzy cross entropy of vague sets. Expert Syst Appl 36(4):8103–8106

    Article  MathSciNet  Google Scholar 

  • Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Modell 53(1–2):91–97

    Article  MathSciNet  MATH  Google Scholar 

  • Ye J (2014a) Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J Intell Fuzzy Syst 26:165–172

    MATH  Google Scholar 

  • Ye J (2014b) Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment. J Intell Fuzzy Syst 27(12):2927–2935

    MathSciNet  Google Scholar 

  • Ye J (2014c) Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int J Fuzzy Syst 16(2):204–211

  • Ye J (2014d) Clustering methods using distance-based similarity measures of single-valued neutrosophic sets. J Intell Syst 23(4):379–389

    Google Scholar 

  • Zadeh LA (1965) Fuzzy Sets. Inf Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, 312000, Zhejiang, People’s Republic of China

    Jun Ye

Authors
  1. Jun Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Ye.

Additional information

Communicated by F. Marcelloni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ye, J. Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Comput 21, 817–825 (2017). https://doi.org/10.1007/s00500-015-1818-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-015-1818-y

Keywords

Search

Navigation