Skip to main content

Power Harmonic Weighted Aggregation Operator on Single-Valued Trapezoidal Neutrosophic Numbers and Interval-Valued Neutrosophic Sets

  • Chapter
  • First Online:
Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 369))

Abstract

The classification of fuzzy sets, intuitionistic fuzzy sets, neutrosophic fuzzy sets have been developed to deal with uncertain, imprecise, incomplete, and inconsistent information data in the real-world situations. Especially the fuzzy numbers are more flexible and suitable to depict the decision information in the process of decision making problem. In multi-criteria decision making (MCDM) And Multi-Criteria Group Decision Making (MCGDM) problems, the aggregation operators play a vital role to deal with these problems. The main contributions of this chapter are to introduce new aggregation operators called Power Harmonic Weighted Aggregation Operator with Single Valued Trapezoidal Neutrosophic Number (PHWAOSVTrNN) and Power Harmonic Weighted Aggregation Operator with Interval-Valued Neutrosophic Set (PHWAOIVNS). To fix the operator on the mount, we have tested these methods in MCDM and the results have been presented.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Das, S., Guha, D.: Power harmonic aggregation operator with trapezoidal intuitionistic fuzzy numbers for solving MAGDM problems. Iran. J. Fuzzy Syst. 12(6), 41–74 (2015)

    MathSciNet  MATH  Google Scholar 

  3. Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Trans Syst. Man Cybern. Part B Cybern. 23, 610–614 (1993)

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Liu, P.D., Teng, F.: Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator. Int. J. Mach. Learn. Cybern. 1–13 (2015)

    Google Scholar 

  6. Liu, C., Luo, Y.: Power aggregation operators of simplified neutrosophic sets and their use in multi-attribute group decision-making. IEEE/CAA J. Automatica Sinica PP(10),1–10 (2017)

    Google Scholar 

  7. Peng, J.J., Wang, J., Wu, X., Wang, J., Chen, X.: Multi-valued neutrosophic sets and power aggregation operators with their applications in multi-criteria group decision-making problems. Int. J. Comput. Intell. Syst. 8(2), 345–363 (2014)

    Article  Google Scholar 

  8. Smarandache, F.: A unifying fields in logics neutrosophic logic. In: Neutrosophy: Neutrosophic Probability Set and Logic. American Research Press, Rehoboth (1999)

    Google Scholar 

  9. Smarandache, F.: A unifying fields in logics neutrosophic logic. In: Neutrosophy, Neutrosophic Set, Neutrosophic Probability, 3rd edn. Xiquan, Phoenix (2003)

    Google Scholar 

  10. Wan, S.P.: Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Appl. Math. Model. 37(6), 4112–4126 (2013)

    Article  MathSciNet  Google Scholar 

  11. Wan, S.P., Dong, J.Y.: Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Appl. Soft Comput. 29, 153–168 (2015)

    Article  Google Scholar 

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

    Google Scholar 

  13. Wei, G.: Some arithmetic aggregation operators with intuitionistic trapezoidal fuzzy numbers and their application to group decision making. J. Comput. 5(3), 345–351 (2010)

    Article  Google Scholar 

  14. Wu, J., Cao, Q.W.: Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl. Math. Model. 37(1), 318–327 (2013)

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  16. Ye, J.: Single valued neutrosophic minimum spanning tree and its clustering method. J. Intell. Fuzzy Syst. 23(3), 311–324 (2014)

    Google Scholar 

  17. Ye, J.: Interval neutrosophic Multiple attribute decision-making method with credibility information. J. Intell. Fuzzy Syst. 18(5), 914–923 (2015)

    Article  Google Scholar 

  18. Zadeh, L.A.: Fuzzy Set. Inf. Control 8, 338–356 (1965)

    Article  Google Scholar 

  19. Zhao, A.W., Du, J.G., Guan, H.J.: Interval valued neutrosophic sets and multi-criteria decision-making based on generalized weighted aggregation operator. J. Intell. Fuzzy Syst. 29(6), 2697–2706 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

The authors express their gratitude to the anonymous reviewer for his/her valuable suggestions in improving the presentation of the chapter.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Janani Bharatraj .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bharatraj, J., Anand, M.C.J. (2019). Power Harmonic Weighted Aggregation Operator on Single-Valued Trapezoidal Neutrosophic Numbers and Interval-Valued Neutrosophic Sets. In: Kahraman, C., Otay, İ. (eds) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Studies in Fuzziness and Soft Computing, vol 369. Springer, Cham. https://doi.org/10.1007/978-3-030-00045-5_3

Download citation

Publish with us

Policies and ethics