Advertisement

(Directed) Hypergraphs: q-Rung Orthopair Fuzzy Models and Beyond

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

Abstract

The q-rung orthopair fuzzy set is a powerful tool for depicting fuzziness and uncertainty, as compared to the Pythagorean fuzzy model. In this chapter, we present concepts including q-rung orthopair fuzzy hypergraphs, \((\alpha , \beta )\)-level hypergraphs, and transversals and minimal transversals of q-rung orthopair fuzzy hypergraphs. We implement some interesting notions of q-rung orthopair fuzzy hypergraphs into decision-making. We describe additional concepts like q-rung orthopair fuzzy directed hypergraphs, dual directed hypergraphs, line graphs, and coloring of q-rung orthopair fuzzy directed hypergraphs.

References

  1. 1.
    Akram, A., Dar, J.M., Naz, S.: Certain graphs under Pythagorean fuzzy environment. Complex Intell. Syst. 5(2), 127–144 (2019)CrossRefGoogle Scholar
  2. 2.
    Akram, M., Ilyasa, F., Garg, H.: Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput. (2019).  https://doi.org/10.1007/s00500-019-04105-0
  3. 3.
    Akram, M., Dar, J.M., Naz, S.: Pythagorean Dombi fuzzy graphs. Complex Intell. Syst. (2019).  https://doi.org/10.1007/s40747-019-0109-0CrossRefGoogle Scholar
  4. 4.
    Akram, M., Habib, A., Davvaz, B.: Direct sum of \(n\) Pythagorean fuzzy graphs with application to group decision-making. J. Mult.-Valued Log. Soft Comput. 1–41 (2019)Google Scholar
  5. 5.
    Akram, M., Naz, S.: A novel decision-making approach under complex Pythagorean fuzzy environment. Math. Comput. Appl. 24(3), 73 (2019)MathSciNetGoogle Scholar
  6. 6.
    Akram, M., Naz, S., Davvaz, B.: Simplified interval-valued Pythagorean fuzzy graphs with application. Complex Intell. Syst. 5(2), 229–253 (2019)CrossRefGoogle Scholar
  7. 7.
    Akram, M., Ilyas, F., Saeid, A.B.: Certain notions of Pythagorean fuzzy graphs. J. Intell. Fuzzy Syst. 36(6), 5857–5874 (2019)CrossRefGoogle Scholar
  8. 8.
    Akram, M., Dudek, W.A., Ilyas, F.: Group decision making based on Pythagorean fuzzy TOPSIS method. Int. J. Intell. Syst. 34(7), 1455–1475 (2019)CrossRefGoogle Scholar
  9. 9.
    Akram, M, Habib , A., Koam , A.N.: A novel description on edge-regular \(q\)-rung picture fuzzy graphs with application. Symmetry 11(4), 489 (2019).  https://doi.org/10.3390/sym110
  10. 10.
    Akram, M., Habib, A., Ilyas, F., Dar, J.M.: Specific types of Pythagorean fuzzy graphs and application to decision-making. Math. Comput. Appl. 23, 42 (2018)MathSciNetGoogle Scholar
  11. 11.
    Akram, M., Naz, S.: Energy of Pythagorean fuzzy graphs with applications. Mathematics 6, 560 (2018).  https://doi.org/10.3390/math6080136CrossRefzbMATHGoogle Scholar
  12. 12.
    Ali, M.I.: Another view on \(q\)-rung orthopair fuzzy sets. Int. J. Intell. Syst. 33, 2139–2153 (2018)CrossRefGoogle Scholar
  13. 13.
    Alkouri, A., Salleh, A.: Complex intuitionistic fuzzy sets. AIP Conf. Proc. 14, 464–470 (2012)CrossRefGoogle Scholar
  14. 14.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)CrossRefGoogle Scholar
  15. 15.
    Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)zbMATHGoogle Scholar
  16. 16.
    Gallo, G., Longo, G., Pallottino, S.: Directed hypergraphs and applications. Discret. Appl. Math. 42, 177–201 (1993)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Goetschel Jr., R.H., Craine, W.L., Voxman, W.: Fuzzy transversals of fuzzy hypergraphs. Fuzzy Sets Syst. 84, 235–254 (1996)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Habib, A., Akram, M.M.: Farooq, \(q\)-rung orthopair fuzzy competition graphs with application in the soil ecosystem. Mathematics 7(1), 91 (2019).  https://doi.org/10.3390/math70100
  19. 19.
    Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, vol. 1. Masson, Paris (1977)Google Scholar
  20. 20.
    Li, L., Zhang, R., Wang, J., Shang, X., Bai, K.: A novel approach to multi-attribute group decision-making with \(q\)-rung picture linguistic information. Symmetry 10(5), 172 (2018)CrossRefGoogle Scholar
  21. 21.
    Liu, P.D., Wang, P.: Some \(q\)-rung orthopair fuzzy aggregation operators and their applications to multi-attribute decision making. Int. J. Intell. Syst. 33, 259–280 (2018)Google Scholar
  22. 22.
    Luqman, A., Akram, M., Al-Kenani, A.N.: \(q\)-rung orthopair fuzzy hypergraphs with applications. Mathematics 7, 260 (2019)CrossRefGoogle Scholar
  23. 23.
    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
  24. 24.
    Luqman, A., Akram, M., Davvaz, B.: \(q\)-rung orthopair fuzzy directed hypergraphs: a new model with applications. J. Intell. Fuzzy Syst. 37, 3777–3794 (2019)CrossRefGoogle Scholar
  25. 25.
    Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)zbMATHGoogle Scholar
  26. 26.
    Myithili, K.K., Parvathi, R.: Transversals of intuitionistic fuzzy directed hypergraphs. Notes Intuit. Fuzzy Sets 21(3), 66–79 (2015)zbMATHGoogle Scholar
  27. 27.
    Naz, S., Ashraf, S., Akram, M.: A novel approach to decision-making with Pythagorean fuzzy information. Mathematics 6(6), 95 (2018).  https://doi.org/10.3390/math6060095CrossRefGoogle Scholar
  28. 28.
    Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)CrossRefGoogle Scholar
  29. 29.
    Ramot, D., Friedman, M., Langholz, G., Kandel, A.: Complex fuzzy logic. IEEE Trans. Fuzzy Syst. 11(4), 450–461 (2003)CrossRefGoogle Scholar
  30. 30.
    Thirunavukarasu, P., Suresh, R., Viswanathan, K.K.: Energy of a complex fuzzy graph. Int. J. Math. Sci. Eng. Appl. 10, 243–248 (2016)Google Scholar
  31. 31.
    Ullah, K., Mahmood, T., Ali, Z., Jan, N.: On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell. Syst. 1–13 (2019)Google Scholar
  32. 32.
    Yager, R.R.: Pythagorean fuzzy subsets. In: Proceedings of the Joint IFSA World Congress and NAIFPS Annual Meeting, Edmonton, Canada, pp. 57–61 (2013)Google Scholar
  33. 33.
    Yager, R.R., Abbasov, A.M.: Pythagorean membership grades, complex numbers and decision making. Int. J. Intell. Syst. 28(5), 436–452 (2013)CrossRefGoogle Scholar
  34. 34.
    Yager, R.R.: Pythagorean membership grades in multi-criteria decision making. IEEE Trans. Fuzzy Syst. 22(4), 958–965 (2014)CrossRefGoogle Scholar
  35. 35.
    Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25, 1222–1230 (2017)CrossRefGoogle Scholar
  36. 36.
    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
  37. 37.
    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