Skip to main content
SpringerLink
Log in

New similarity and entropy measures of single-valued neutrosophic sets with applications in multi-attribute decision making

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

Abstract

Information measures play a fundamental role in single-valued neutrosophic set (SVNS) theory. The main purpose of this paper is to study the similarity and entropy measures of SVNS with applications in multi-attribute decision making. We proposed the axiomatic definitions of similarity and entropy for single-valued neutrosophic values (SVNVs) with respect to a new kind of inclusion relation between SVNVs. On the basis of Hamming distance, cosine function and cotangent function, three similarity measures and three entropies for SVNVs are constructed. Then, we extended the definitions and construction methods of similarity and entropy for SVNVs to SVNSs by using some aggregation operators. Finally, by using the new similarity and entropy measures we presented a SVNSs based multi-attribute decision making method. It demonstrated that the new information measures presented in this study are applicable and efficient.

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

  • Abualigah LM (2019) Feature selection and enhanced krill herd algorithm for text document clustering-studies in computational intelligence. Springer, Berlin

    Book  Google Scholar 

  • Abualigah LM, Hanandeh ES (2015) Applying genetic algorithms to information retrieval using vector space model. Int J Comput Sci Eng Appl 1(5):19–28

    Google Scholar 

  • Abualigah LM, Khader AT (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. J Supercomput 73(11):4773–4795

    Article  Google Scholar 

  • Abualigah LM, Khader AT, Hanandeh ES (2018a) A combination of objective functions and hybrid krill herd algorithm for text document clustering analysis. Eng Applic Artif Intell 73:111–125

    Article  Google Scholar 

  • Abualigah LM, Khader AT, Hanandeh ES (2018b) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466

    Article  Google Scholar 

  • Abualigah LM, Khader AT, Hanandeh ES (2018c) Hybrid clustering analysis using improved krill herd algorithm. Appl Intell 48(11):4047–4071

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  • Borzooei RA, Farahani H, Moniri M (2014) Neutrosophic deductive filters on BL-algebras. J Intell Fuzzy Syst 26:2993–3004

    Article  MathSciNet  MATH  Google Scholar 

  • Crispin Sweety CA, Arockiarani I (2017) Rough sets in neutrosophic approximation space. Ann Fuzzy Math Inform 13(4):449–463

    Article  MATH  Google Scholar 

  • Deli I (2017) Interval-valued neutrosophic soft sets and its decision making. Int J Mach Learn Cybern 8:665–676

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Jun YB, Smarandache F, Kim CS (2017) Neutrosophic cubic sets. New Math Nat Comput 13(1):41–54

    Article  MATH  Google Scholar 

  • Liu PD, Shi L (2015) The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making. Neural Comput Appl 26(2):457–471

    Article  Google Scholar 

  • Liu YL, Yang HL (2017) Further research of single valued neutrosophic rough sets. J Intell Fuzzy Syst 33:1467–1478

    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 

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

    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 

  • Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2016) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci 47(10):2342–2358

    Article  MATH  Google Scholar 

  • Pramanik S, Dalapati S, Alam S, Smarandache F, Roy TK (2018) NS-cross entropy-based MAGDM under single-valued neutrosophic set environment. Information 9:37. https://doi.org/10.3390/info9020037

    Article  Google Scholar 

  • Sahin R (2017) Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Comput Appl 28:1177–1187

    Article  Google Scholar 

  • Singh PK (2017) Three-way fuzzy concept lattice representation using neutrosophic set. Int J Mach Learn Cybern 8(1):69–79

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Smarandache F (2005) Neutrosophic set-a generialization of the intuitionistics fuzzy sets. Int J Pure Appl Math 24(3):287–297

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Wu HB, Yuan Y, Wei LJ, Pei LD (2018) On entropy, similarity measure and cross-entropy of single-valued neutrosophic sets and their application in multi-attribute decision making. Soft Comput 22:7367–7376

    Article  Google Scholar 

  • Yang HL, Zhang CL, Guo ZL, Liu YL, Liao XW (2017) A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model. Soft Comput 21(21):6253–6267

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Ye J (2015) Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Artif Intell Med 63(3):171–179

    Article  Google Scholar 

  • Ye J (2016) Fault diagnoses of steam turbine using the exponential similarity measure of neutrosophic numbers. J Intell Fuzzy Syst 30(4):1927–1934

    Article  MATH  Google Scholar 

  • Ye J (2017a) Simplified neutrosophic harmonic averaging projection-based method for multiple attribute decision making problems. Int J Mach Learn Cybern 8(3):981–987

    Article  Google Scholar 

  • Ye J (2017b) Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Comput 21(3):817–825

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Zhan JM, Khan M, Gulistan M, Ali A (2017) Applications of neutrosophic cubic sets in multi-criteria decision-making. Int J Uncertain Quantif 7(5):377–394

    Article  Google Scholar 

  • Zhang XH (2017a) Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras. J Intell Fuzzy Syst 33:1767–1774

    Article  MATH  Google Scholar 

  • Zhang XH, Ma YC, Smarandache F (2017b) Neutrosophic regular filters and fuzzy regular filters in pseudo-BCI algebras. Neutrosophic Sets Syst 17:10–15

    Google Scholar 

  • Zhang XH, Bo CX, Smarandache F, Dai JH (2018a) New inclusion relation of neutrosophic sets with applications and related lattice structure. Int J Mach Learn Cybern 9(10):1753–1763

    Article  Google Scholar 

  • Zhang XH, Bo CX, Smarandache F, Park C (2018b) New operations of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets. Symmetry 10:187. https://doi.org/10.3390/sym10060187

    Article  Google Scholar 

  • Zhang XH, Yu P, Smarandache F, Park C (2018c) Redefined neutrosophic filters in BE-algebras. Ital J Pure Appl Math (in press)

Download references

Acknowledgements

This work has been partially supported by the National Natural Science Foundation of China (Grant Nos. 61976130, 61473239).

Author information

Authors and Affiliations

  1. College of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Keyun Qin & Lu Wang

Authors
  1. Keyun Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lu Wang.

Ethics declarations

Conflict of interest

This article does not contain any studies with human participants or animals performed by any of the authors. Furthermore the authors declare that there are no conflicts of interest.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, K., Wang, L. New similarity and entropy measures of single-valued neutrosophic sets with applications in multi-attribute decision making. Soft Comput 24, 16165–16176 (2020). https://doi.org/10.1007/s00500-020-04930-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-04930-8

Keywords

Search

Navigation