Skip to main content
SpringerLink
Log in

A new decision-making method based on bipolar neutrosophic directed hypergraphs

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

Directed hypergraphs are widely used as a tool to solve and model the problems appearing in computer science and operations research. Bipolar neutrosophic models are more flexible and applicable because these models study neutrosophic behavior positively as well as negatively. In this research study, we present a new frame work for handling bipolar neutrosophic information by combining the bipolar neutrosophic sets with directed hypergraphs. We introduce certain new concepts, including bipolar neutrosophic directed hypergraphs, regular bipolar neutrosophic directed hypergraphs, homomorphism and isomorphism on bipolar neutrosophic directed hypergraphs. Further, we study some isomorphic properties of strong bipolar neutrosophic directed hypergraphs. In particular, we consider interesting applications of bipolar neutrosophic directed hypergraphs in decision-making, and we develop efficient algorithm to solve decision-making problems.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Akram, M.: Bipolar fuzzy graphs. Inf. Sci. 181(24), 5548–5564 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Akram, M., Luqman, A.: Certain concepts of bipolar fuzzy directed hypergraphs. Mathematics 5(1), 1–18 (2017)

    Article  MATH  Google Scholar 

  3. Akram, M., Luqman, A.: Bipolar neutrosophic hypergraphs with applications. J. Intell. Fuzzy Syst. 33 (2017), in press

  4. Akram, M., Luqman, A.: Certain networks models using single-valued neutrosophic directed hypergraphs. J. Intell. Fuzzy Syst. (2017). doi:10.3233/JIFS-162347

  5. Akram, M., Luqman, A.: Intuitionistic single-valued neutrosophic hypergraphs. OPSEARCH (2017). doi:10.1007/s12597-017-0306-9

  6. Akram, M., Alshehri, N., Davvaz, B., Ashraf, A.: Bipolar fuzzy digraphs in decision support systems. J. Multi-Valued Logic Soft Comput. 27, 531–551 (2016)

    Google Scholar 

  7. Akram, M., Dudek, W.A., Sarwar, S.: Properties of bipolar fuzzy hypergraphs. Ital. J. Pure Appl. Math. 31, 141–160 (2013)

    MathSciNet  MATH  Google Scholar 

  8. Akram, M., Sarwar, M.: Novel multiple criteria making methods based on bipolar neutrosophic sets and bipolar neutrosophic graphs. Ital. J. Pure Appl. Math. 38, 1–22 (2017)

    MATH  Google Scholar 

  9. Akram, M., Sarwar, M.: Novel applications of \(m\)-polar fuzzy hypergraphs. J. Intell. Fuzzy Syst. 32(3), 2747–2762 (2017)

    Article  MATH  Google Scholar 

  10. Akram, M., Shahzadi, S.: Neutrosophic soft graphs with application. J. Intell. Fuzzy Syst. 32(1), 841–858 (2017)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  12. Berge, C.: Graphs and Hypergraphs. North-Holland Publishing Company, Amsterdam (1973)

    MATH  Google Scholar 

  13. Broumi, S., Talea, M., Bakali, A., Smarandache, F.: On bipolar single valued neutrosophic graphs. J. New Theory 11, 84–102 (2016)

    Google Scholar 

  14. Chen, S.M.: Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst. Man Cybern. (Cybern.) 27(4), 725–733 (1997)

    Article  Google Scholar 

  15. Deli, I., Ali, M., Smarandache, F.: Bipolar neutrosophic sets and their applications based on multi-criteria decision making problems. In: Advanced Mechatronic Systems (ICAMechS), International Conference IEEE, pp. 249–254 (2015)

  16. Gallo, G., Longo, G., Pallottino, S.: Directed hypergraphs and applications. Discrete Appl. Math. 42, 177–201 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kaufmann, A.: Introduction a la Theorie des Sous-Ensemble Flous, 1. Masson, Paris (1977)

    MATH  Google Scholar 

  18. Lee, K.-M.: Bipolar-valued fuzzy sets and their basic operations. In: Proceedings of International Conference, Bangkok, Thailand, pp. 307–317 (2000)

  19. Lee-kwang, H., Lee, K.-M.: Fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst Man Cybern. 25(1), 196–201 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mordeson, J.N., Nair, P.S.: Fuzzy graphs and fuzzy hypergraphs. Physica, Heidelberg, Second Edition 2001 (1998)

  21. Myithili, K.K., Parvathi, R., Akram, M.: Certain types of intuitionistic fuzzy directed hypergraphs. Int. J. Mach. Learn. Cybern. 7, 287–295 (2016)

    Article  MATH  Google Scholar 

  22. Parvathi, R., Karunambigai, M. G.: Intuitionistic fuzzy graphs. In: Computational Intelligence, Theory and applications, International Conference in Germany, pp. 18–20 (2006)

  23. Parvathi, R., Thilagavathi, S.: Intuitionistic fuzzy directed hypergraphs. Adv. Fuzzy Sets Syst. 14, 39–52 (2013)

    MathSciNet  MATH  Google Scholar 

  24. Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and Their Applications, pp. 77–95. Academic Press, New York (1975)

    Google Scholar 

  25. Radhamani, C., Radhika, C.: Isomorphism on fuzzy hypergraphs. IOSR J. Math. 2(6), 24–31 (2012)

    Google Scholar 

  26. Radhika, C., Radhamani, C., Suresh, S.: Isomorphism properties on strong fuzzy hypergraphs. Int. J. Comput. Appl. 64(1), 23–27 (2013)

    Google Scholar 

  27. Smarandache, F.: Neutrosophy, Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1998)

    MATH  Google Scholar 

  28. Samanta, S., Pal, M.: Bipolar fuzzy hypergraphs. Int. J. Fuzzy Logic Syst. 2(1), 17–28 (2012)

    Article  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  32. Zhang, W.R.: Bipolar fuzzy sets. In: Fuzzy Systems Proceedings, IEEE World Congress on Computational Intelligence (1998)

  33. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors are highly thankful to to Editor-in-Chief and the referees for their valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram & Anam Luqman

Authors
  1. Muhammad Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anam Luqman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Akram.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akram, M., Luqman, A. A new decision-making method based on bipolar neutrosophic directed hypergraphs. J. Appl. Math. Comput. 57, 547–575 (2018). https://doi.org/10.1007/s12190-017-1121-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-017-1121-4

Keywords

Mathematics Subject Classification

Search

Navigation