Skip to main content
SpringerLink
Log in

COPRAS Method with 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

Interval neutrosophic number (INN), which is descripted by the degree of truth-membership, indeterminacy-membership and falsity-membership of an element, is a powerful information tool with many application areas. The purpose of this study is to develop an extended form of COPRAS (Complex Proportional Assessment) method used for solving the decision making problems in which all the data presented by decision makers is in the form of interval neutrosophic matrix presented by INNs, and the information about criterion weights is partially known or completely unknown. In order to accomplish this goal, a new score function and an accuracy function that consider the decision maker’s risk attitude are defined under a parameter called the risk index to determine the ordering of INNs. Then, based on Maclaurin symmetric mean (MSM) operator that can capture the interrelationships among multi-input arguments, some aggregation operators are defined, such as interval neutrosophic Maclaurin symmetric mean (INMSM) operator and interval neutrosophic weighted Maclaurin symmetric mean (INWMSM) operator. Moreover, some optimization models are established to determine the subjective and objective weights of decision criteria. A numerical problem is solved to demonstrate the effective and feasible structure of the developed method. Then, a sensitive analysis is conducted according to the decision maker’s risk attitude, and the advantages of the developed method are listed. Finally, a comparison analysis is provided to present the relationships among the developed method and existing methods, and some conclusions are given at the end of the study.

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

Access this chapter

Log in via an institution
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. Atanassov, K., Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)

    Article  MathSciNet  Google Scholar 

  3. Broumi, S., Smarandache, F.: Correlation coefficient of interval neutrosophic set. Appl. Mech. Mater. 436, 511–517 (2013)

    Article  Google Scholar 

  4. Broumi, S., Smarandache, F.: Cosine similarity measure of interval valued neutrosophic sets. Neutrosophic Sets Syst. 5, 15–20 (2014)

    Google Scholar 

  5. Biswas, P., Pramanik, S., Giri, B.C.: TOPSIS method for multi-criteria group decision-making under simplified neutrosophic environment. Neural Comput. Appl. 27(3), 727–737 (2016)

    Article  Google Scholar 

  6. Beliakov, G., James, S.: On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts. Fuzzy Sets Syst. 211, 84–98 (2013)

    Article  MathSciNet  Google Scholar 

  7. Chi, P., Liu, P.: An extended TOPSIS method for the multiple attribute decision making problems based on interval neutrosophic set. Neutrosophic Sets Syst. 1, 63–70 (2013)

    Google Scholar 

  8. Hashemkhani Zolfani, S., Rezaeiniya, N., Aghdaie, M.H., Zavadskas, E.K.: Quality control manager selection based on AHP-COPRAS-G methods: a case in Iran. Ekonomska istrazivanja Econ. Res. 25(1), 88–104 (2012)

    Google Scholar 

  9. Liu, P.D., Wang, Y.: Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making. J. Syst. Sci. Complex. 29, 681–697 (2016)

    Article  Google Scholar 

  10. Liu, P.D., Tang, G.: Some power generalized aggregation operators based on the interval neutrosophic sets and their application to decision making. J. Intell. Fuzzy Syst. 30(5), 2517–2528 (2016)

    Article  MathSciNet  Google Scholar 

  11. Maclaurin, C.A.: Second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philos. Trans. R. Soc. Lond. Ser. A 36, 59–96 (1729)

    Google Scholar 

  12. Razavi Hajiagha, S.H., Hashemi, S.S., Zavadskas, E.K.: A complex proportional assessment method for group decision making in an interval-valued intuitionistic fuzzy environment. Technol. Econ. Dev. Econ. 19(1), 22–37 (2013)

    Article  Google Scholar 

  13. Qin, J., Liu, X.: An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J. Intell. Fuzzy Syst. 27(5), 2177–2190 (2015)

    MathSciNet  MATH  Google Scholar 

  14. Smarandache, F.: A generalization of the intuitionistic fuzzy set. Int. J. Pure Appl. Math. 24, 287–297 (2005)

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  16. Şahin, R.: Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Comput. Appl. 28(5), 1177–1187 (2017)

    Article  Google Scholar 

  17. Tian, Z.P., Zhang, H.Y., Wang, J., Wang, J.Q., Chen, X.H.: Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int. J. Syst. Sci. 47(15), 3598–3608 (2016)

    Article  Google Scholar 

  18. Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R.: Single valued neutrosophic sets. Multispace Multistructure 4, 410–413 (2010)

    MATH  Google Scholar 

  19. Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R.: Interval Neutrosophic Sets and Logic: Theory and Applications in Computing’. Hexis, Phoenix, AZ (2005)

    MATH  Google Scholar 

  20. Xiaoli, L.: An approach to interval-valued intuitionistic fuzzy multiple attribute decision making based on the MSM operator and their applications to online advertising publisher evaluation. J. Comput. Theor. Nanosci. 13(10), 7280–7284 (2016)

    Article  Google Scholar 

  21. Ye, J.: Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J. Intell. Fuzzy Syst. 26(1), 165–172 (2014)

    MATH  Google Scholar 

  22. Ye, J.: Interval neutrosophic multiple attribute decision-making method with credibility information. Int. J. Fuzzy Syst. 18(5), 914–923 (2016)

    Article  Google Scholar 

  23. Ye, J.: Multi-criteria decision-making method based on the possibility degree ranking method and ordered weighted aggregation operators of interval neutrosophic numbers. J. Intell. Fuzzy Syst. 28(3), 1307–1317 (2015)

    Google Scholar 

  24. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  25. Zavadskas, E.K., Kaklauskas, A., Sarka, V.: The new method of multicriteria complex proportional assessment of projects. Technol. Econ. Dev. Econ. 1(3), 131–139 (1994)

    Google Scholar 

  26. Zavadskas, E.K., Kaklauskas, A., Peldschus, F., Turskis, Z.: Multi-attribute assessment of road design solution by using the COPRAS method. Baltic J. Road Bridge Eng. 2(4), 195–203 (2007)

    Google Scholar 

  27. Zhang, H., Wang, J.Q., Chen, X.H.: An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Comput. Appl. 27(3), 615–627 (2015)

    Article  Google Scholar 

  28. Zhang, H.Y., Wang, J.Q., Chen, X.H.: Interval neutrosophic sets and their application in multicriteria decision making problems, Sci. Word J. Article ID 645953 (2014)

    Google Scholar 

  29. Zhu, B., Xu, Z.S.: Hesitant fuzzy Bonferroni means for multicriteria decision making. J. Oper. Res. Soc. 64(12), 1831–1840 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Engineering, Faculty of Engineering and Natural Sciences, Gümüşhane University, Gümüşhane, Turkey

    Rıdvan Şahin

Authors
  1. Rıdvan Şahin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rıdvan Şahin .

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, Macka, Istanbul, Turkey

    Cengiz Kahraman

  2. Department of Industrial Engineering, Istanbul Okan University, Akfirat-Tuzla, Istanbul, Turkey

    İrem Otay

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

Şahin, R. (2019). COPRAS Method with 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_19

Download citation

Publish with us

Policies and ethics

Search

Navigation