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Hypergraphs in Intuitionistic Fuzzy Environment

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

Abstract

In this Chapter, we define intuitionistic fuzzy hypergraphs, dual intuitionistic fuzzy hypergraphs, intuitionistic fuzzy line graphs, and 2-section of an intuitionistic fuzzy hypergraph. We describe some applications of intuitionistic fuzzy hypergraphs in planet surface networks, intersecting communities in a social network, grouping of incompatible chemical substances, and clustering problems. We design certain algorithms to construct dual intuitionistic fuzzy hypergraphs, intuitionistic fuzzy line graphs, and the selection of objects in decision-making problems. Further, we present the concept of intuitionistic fuzzy directed hypergraphs and complex intuitionistic fuzzy hypergraphs. This Chapter is basically due to [2, 3, 6, 12, 14, 15, 17, 18].

References

  1. 1.
    Akram, M., Davvaz, B.: Strong intuitionistic fuzzy graphs. FILOMAT 26(1), 177–196 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Akram, M., Dudek, W.A.: Intuitionistic fuzzy hypergraphs with applications. Inf. Sci. 218, 182–193 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Akram, M., Sarwar, M., Borzooei, R.A.: A novel decision-making approach based on hypergraphs in intuitionistic fuzzy environment. J. Intell. Fuzzy Syst. 35(2), 1905–1922 (2018)CrossRefGoogle Scholar
  4. 4.
    Alkouri, A., Salleh, A.: Complex intuitionistic fuzzy sets. AIP Conf. Proc. 14, 464–470 (2012)Google Scholar
  5. 5.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)zbMATHGoogle Scholar
  6. 6.
    Atanassov, K.T.: Intuitionistic fuzzy sets: theory and applications. Studies in Fuzziness and Soft Computing, vol. 35. Physica-Verl, Heidelberg, New York (1999)Google Scholar
  7. 7.
    Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)zbMATHGoogle Scholar
  8. 8.
    Chen, S.M., Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst. Man Cybern. (Cybernetics) 27(4), 725–733 (1997)Google Scholar
  9. 9.
    Gallo, G., Longo, G., Pallottino, S.: Directed hypergraphs and applications. Discret. Appl. Math. 42, 177–201 (1993)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, vol. 1. Masson, Paris (1977)Google Scholar
  11. 11.
    Lee-Kwang, H., Lee, K.-M.: Fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst. Man Cybern. 25(1), 196–201 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Luqman, A., Akram, M., Al-Kenani, A.N., Alcantud, J.C.R.: A study on hypergraph representations of complex fuzzy information. Symmetry 11(11), 1381 (2019)CrossRefGoogle Scholar
  13. 13.
    Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)zbMATHGoogle Scholar
  14. 14.
    Myithili, K.K., Parvathi, R.: Transversals of intuitionistic fuzzy directed hypergraphs. Notes Intuit. Fuzzy Sets 21(3), 66–79 (2015)zbMATHGoogle Scholar
  15. 15.
    Myithili, K.K., Parvathi, R., Akram, M.: Certain types of intuitionistic fuzzy directed hypergraphs. Int. J. Mach. Learn. Cybern. 7(2), 287–295 (2016)CrossRefGoogle Scholar
  16. 16.
    Parvathi, R., Akram, M., Thilagavathi, S.: Intuitionistic fuzzy shortest hyperpath in a network. Inf. Process. Lett. 113(17), 599–603 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Parvathi, R., Thilagavathi, S., Karunambigai, M.G.: Intuitionistic fuzzy hypergraphs. Cybern. Inf. Technol. 9(2), 46–53 (2009)MathSciNetGoogle Scholar
  18. 18.
    Parvathi, R., Thilagavathi, S.: Intuitionistic fuzzy directed hypergraphs. Adv. Fuzzy Sets Syst. 14(1), 39–52 (2013)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Parvathi, R., Thilagavathi, S., Atanassov, K.T.: Isomorphism on intuitionistic fuzzy directed hypergraphs. Int. J. Sci. Res. Publ. 3(3) (2013)Google Scholar
  20. 20.
    Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)CrossRefGoogle Scholar
  21. 21.
    Ramot, D., Friedman, M., Langholz, G., Kandel, A.: Complex fuzzy logic. IEEE Trans. Fuzzy Syst. 11(4), 450–461 (2003)CrossRefGoogle Scholar
  22. 22.
    Thirunavukarasu, P., Suresh, R., Viswanathan, K.K.: Energy of a complex fuzzy graph. Int. J. Math. Sci. Eng. Appl. 10(1), 243–248 (2016)Google Scholar
  23. 23.
    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
  24. 24.
    Yazdanbakhsh, O., Dick, S.: A systematic review of complex fuzzy sets and logic. Fuzzy Sets. Syst. 338, 1–22 (2018)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar

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© 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

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