Some Types of Hypergraphs for Single-Valued Neutrosophic Structures

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 390)


In this chapter, we present concepts including single-valued neutrosophic hypergraphs, dual single-valued neutrosophic hypergraphs, and transversal single-valued neutrosophic hypergraphs. Additionally, we discuss the notions of intuitionistic single-valued neutrosophic hypergraphs and dual intuitionistic single-valued neutrosophic hypergraphs. We describe an application of intuitionistic single-valued neutrosophic hypergraphs in a clustering problem.


  1. 1.
    Akram, M.: Single-valued neutrosophic planar graphs. Int. J. Algeb. Stat. 5(2), 157–167 (2016)CrossRefGoogle Scholar
  2. 2.
    Akram, M.: Single-valued neutrosophic graphs. Infosys Science Foundation Series in Mathematical Sciences, pp. 1–373. Springer (2018)Google Scholar
  3. 3.
    Akram, M., Luqman, A.: Intuitionistic single-valued neutrosophic hypergraphs. OPSEARCH 54(4), 799–815 (2017)CrossRefGoogle Scholar
  4. 4.
    Akram, M., Luqman, A.: Certain network models using single-valued neutrosophic directed hypergraphs. J. Intell. Fuzzy Syst. 33(1), 575–588 (2017)CrossRefGoogle Scholar
  5. 5.
    Akram, M., Shahzadi, S., Borumand Saeid, A.: Single-valued neutrosophic hypergraphs. TWMS J. Appl. Eng. Math. 8(1), 122–135 (2018)zbMATHGoogle Scholar
  6. 6.
    Ali, M., Smarandache, F.: Complex neutrosophic set. Neural Comput. Appl. 28(7), 1817–1834 (2017)CrossRefGoogle Scholar
  7. 7.
    Alkouri, A., Salleh, A.: Complex intuitionistic fuzzy sets, AIP Conference Proceedings, vol. 14, pp. 464–470 (2012)Google Scholar
  8. 8.
    Atanassov. K.T., Intuitionistic fuzzy sets. In: VII ITKR’s Session, Sofia (deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84), (1983) (in Bulgarian)Google Scholar
  9. 9.
    Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)zbMATHGoogle Scholar
  10. 10.
    Bhowmik, M., Pal, M.: Intuitionistic neutrosophic set. J. Inf. Comput. Sci. 4(2), 142–152 (2009)Google Scholar
  11. 11.
    Bhowmik, M., Pal, M.: Intuitionistic neutrosophic set relations and some of its properties. J. Inf. Comput. Sci. 5(3), 183–192 (2010)Google Scholar
  12. 12.
    Gallo, G., Longo, G., Pallottino, S.: Directed hypergraphs and applications. Discret. Appl. Math. 42, 177–201 (1993)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, 1. Masson, Paris (1977)Google Scholar
  14. 14.
    Luqman, A., Akram, M. and Smarandache, F.: Complex neutrosophic hypergraphs: new social network models. Algorithms 12(11), 234 (2019)CrossRefGoogle Scholar
  15. 15.
    Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)zbMATHGoogle Scholar
  16. 16.
    Parvathi, R., Thilagavathi, S., Karunambigai, M.G.: Intuitionistic fuzzy hypergraphs. Cybern. Inf. Technol. 9(2), 46–53 (2009)MathSciNetGoogle Scholar
  17. 17.
    Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)CrossRefGoogle Scholar
  18. 18.
    Ramot, D., Friedman, M., Langholz, G., Kandel, A.: Complex fuzzy logic. IEEE Trans. Fuzzy Syst. 11(4), 450–461 (2003)CrossRefGoogle Scholar
  19. 19.
    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
  20. 20.
    Smarandache, F.: Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1998)zbMATHGoogle Scholar
  21. 21.
    Smarandache, F.: A Unifying Field in Logics Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1999)zbMATHGoogle Scholar
  22. 22.
    Smarandache, F.: Neutrosophic set-a generalization of the intuitionistic fuzzy set. Int. J. Pure Appl. Math. 24(3), 287Google Scholar
  23. 23.
    Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R.: Single valued neutrosophic sets. Multispace and Multistructure 4, 410–413 (2010)zbMATHGoogle Scholar
  24. 24.
    Yang, H.L., Guo, Z.L., Liao, X.: On single-valued neutrosophic relations. J. Intell. Fuzzy Syst. 30(2), 1045–1056 (2016)CrossRefGoogle Scholar
  25. 25.
    Yaqoob, N., Akram, M.: Complex neutrosophic graphs. Bull. Comput. Appl. Math. 6(2), 85–109 (2018)Google Scholar
  26. 26.
    Yaqoob, N., Gulistan, M., Kadry, S., Wahab, H.: Complex intuitionistic fuzzy graphs with application in cellular network provider companies. Mathematics 7(1), 35 (2019)CrossRefGoogle Scholar
  27. 27.
    Yazdanbakhsh, O., Dick, S.: A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst. 338, 1–22 (2018)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan
  2. 2.Department of MathematicsUniversity of the PunjabLahorePakistan

Personalised recommendations