Skip to main content
SpringerLink
Log in

A study on some operations and products of neutrosophic hypersoft graphs

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

Abstract

Neutrosophic hypersoft set is the combination of neutrosophic set and hypersoft set. It resolves the limitations of intuitionistic fuzzy sets and soft sets for the consideration of the degree of indeterminacy and multi-argument approximate function respectively. In this research article, a novel framework is formulated for handling neutrosophic hypersoft information by combining the theory of neutrosophic hypersoft sets with graphs. Firstly, different types of notions, including neutrosophic hypersoft graphs, strong neutrosophic hypersoft graphs, complete neutrosophic hypersoft graphs, are characterized with the help of numerical examples and graphical representation. Secondly, some products (i.e. Cartesian product, cross product, lexicographic product, strong product) and composition of neutrosophic hypersoft graphs are discussed by employing various methods of their construction. Moreover, some of their related properties are also investigated. Lastly, an application of neutrosophic hypersoft graph is presented to decision making with the help of proposed algorithm.

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

Similar content being viewed by others

References

  1. Abbas, F., Murtaza, G., Smarandache, F.: Basic operations on hypersoft sets and hypersoft points. Neutrosophic Sets Syst. 35, 407–421 (2020). https://doi.org/10.5281/zenodo.3951694

    Article  Google Scholar 

  2. Akram, M., Shahzadi, S.: Neutrosophic soft graphs with application. J. Intell. Fuzzy Syst. 32(1), 841–858 (2017). https://doi.org/10.3233/jifs-16090

    Article  MATH  Google Scholar 

  3. Alhabib, R., Ranna, M.M., Farah, H., Salama, A.A.: Some neutrosophic probability distributions. Neutrosophic Sets Syst. 22, 30–38 (2018). https://doi.org/10.5281/zenodo.2160479

    Article  Google Scholar 

  4. Ali, M.I., Feng, F., Liu, X., Min, W.K., Sabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009). https://doi.org/10.1016/j.camwa.2008.11.009

    Article  MathSciNet  MATH  Google Scholar 

  5. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986). https://doi.org/10.1016/S0165-0114(86)80034-3

    Article  MATH  Google Scholar 

  6. Babitha, K.V., Sunil, J.J.: Soft set relations and functions. Comput. Math. Appl. 60, 1840–1849 (2010). https://doi.org/10.1016/j.camwa.2010.07.014

    Article  MathSciNet  MATH  Google Scholar 

  7. Babitha, K.V., Sunil, J.J.: Transitive closure and ordering in soft set. Comput. Math. Appl. 61, 2235–2239 (2011). https://doi.org/10.1016/j.camwa.2011.07.010

    Article  MATH  Google Scholar 

  8. Broumi, S., Bakali, A., Talea, M., Smarandache, F., Karaaslan, F.: Interval valued neutrosophic soft graphs. New Trends Neutrosophic Theory Appl. (2016). https://doi.org/10.5281/zenodo.1410271

    Article  Google Scholar 

  9. Broumi, S., Smarandache, F.: Intuitionistic neutrosophic soft set. J. Inf. Comput. Sci. 8(2), 130–140 (2013). https://doi.org/10.5281/zenodo.2861554

    Article  Google Scholar 

  10. Broumi, S.: Generalized neutrosophic soft set. Int. J. Comput. Sci. Eng. Inf. Technol. 3(2), 17–30 (2013). https://doi.org/10.5121/ijcseit.2013.3202

    Article  Google Scholar 

  11. Broumi, S., Deli, I., Smarandache, F.: Relations on interval valued neutrosophic soft sets. J. New Results Sci. 5, 1–20 (2014). https://doi.org/10.5281/zenodo.30306

    Article  MATH  Google Scholar 

  12. Deli, I.: Interval-valued neutrosophic soft sets and its decision making. Int. J. Mach. Learn. Cybern. 8(2), 665–676 (2017). https://doi.org/10.1007/s13042-015-0461-3

    Article  MathSciNet  Google Scholar 

  13. Ge, X., Yang, S.: Investigations on some operations of soft sets. World Acad. Sci. Eng. Technol. 75, 1113–1116 (2011)

    Google Scholar 

  14. Hussain, S.S., Hussain, R., Smarandache, F.: Domination number in neutrosophic soft graphs. Neutrosophic Sets Syst. 28, 228–244 (2019). https://doi.org/10.5281/zenodo.3382548

    Article  Google Scholar 

  15. Kharal, A.: A neutrosophic multicriteria decision making method. New Math. Nat. Comput. 10(2), 143–162 (2014). https://doi.org/10.1142/S1793005714500070

    Article  MathSciNet  Google Scholar 

  16. Li, F.: Notes on soft set operations. ARPN J. Syst. Softw. 1, 205–208 (2011)

    Article  Google Scholar 

  17. Maji, P.K., Biswas, R., Roy, A.R.: Soft set theory. Comput. Math. Appl. 45, 555–562 (2003). https://doi.org/10.1016/S0898-1221(03)00016-6

    Article  MathSciNet  MATH  Google Scholar 

  18. Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. J. Fuzzy Math. 9(3), 589–602 (2001)

    MathSciNet  MATH  Google Scholar 

  19. Maji, P.K., Biswas, R., Roy, A.R.: Intuitionistic fuzzy soft sets. J. Fuzzy Math. 9(3), 677–692 (2001)

    MathSciNet  MATH  Google Scholar 

  20. Maji, P.K.: Neutrosophic soft set. Ann. Fuzzy Math. Inform. 5(1), 157–168 (2013)

    MathSciNet  MATH  Google Scholar 

  21. Martin, N., Smarandache, F.: Concentric plithogenic hypergraph based on plithogenic hypersoft sets a novel outlook. Neutrosophic Sets Syst. 33, 78–91 (2020). https://doi.org/10.5281/zenodo.3782824

    Article  Google Scholar 

  22. Molodtsov, D.: Soft set theory—first results. Comput. Math. Appl. 37, 19–31 (1999). https://doi.org/10.1016/S0898-1221(99)00056-5

    Article  MathSciNet  MATH  Google Scholar 

  23. Pei, D., Miao, D.: From soft set to information system. IEEE Int. Conf. Granul. Comput. 2, 617–621 (2005). https://doi.org/10.1109/GRC.2005.1547365

    Article  Google Scholar 

  24. Pramanik, S., Dey, P.P., Smarandache, F.: Correlation coeficient measures of interval bipolar neutrosophic sets for solving multi-attribute decision making problems. Neutrosophic Sets Syst. 19, 70–79 (2018). https://doi.org/10.5281/zenodo.1235151

    Article  Google Scholar 

  25. Rahman, A.U., Saeed, M., Zahid, S.: Application in decision making based on fuzzy parameterized hypersoft set theory. Asia Mathematika 5(1), 19–27 (2021). https://doi.org/10.5281/zenodo.4721481

    Article  Google Scholar 

  26. Rahman, A.U., Saeed, M., Dhital, A.: Decision making application based on neutrosophic parameterized hypersoft set theory. Neutrosophic Sets Syst. 41, 1–14 (2021). https://doi.org/10.5281/zenodo.4625665

    Article  Google Scholar 

  27. Rahman, A.U., Saeed, M., Smarandache, F., Ahmad, M.R.: Development of hybrids of hypersoft set with complex fuzzy set, complex intuitionistic fuzzy set and complex neutrosophic set. Neutrosophic Sets Syst. 38, 335–354 (2020). https://doi.org/10.5281/zenodo.4300520

    Article  Google Scholar 

  28. Rahman, A.U., Saeed, M., Smarandache, F.: Convex and concave hypersoft sets with some properties. Neutrosophic Sets Syst. 38, 497–508 (2020). https://doi.org/10.5281/zenodo.4300580

    Article  Google Scholar 

  29. Saeed, M., Ahsan, M., Siddique, M.K., Ahmad, M.R.: A study of the fundamentals of hypersoft set theory. Int. J. Sci. Eng. Res. 11(1), 320–329 (2020)

    Google Scholar 

  30. Saeed, M., Rahman, A.U., Ahsan, M., Smarandache, F.: An inclusive study on fundamentals of hypersoft set. In: Smarandache, F., Saeed, M., Abdel-Baset, M., Saqlain, M. (eds.) Theory and Application of Hypersoft Set. pp. 1–23. Pons Publishing House, Brussels (2021)

  31. Saqlain, M., Jafar, N., Moin, S., Saeed, M., Broumi, S.: Single and multi-valued neutrosophic hypersoft set and tangent similarity measure of single valued neutrosophic hypersoft sets. Neutrosophic Sets Syst. 32, 317–329 (2020). https://doi.org/10.5281/zenodo.3723165

    Article  Google Scholar 

  32. Saqlain, M., Moin, S., Jafar, N., Saeed, M., Smarandache, F.: Aggregate operators of neutrosophic hypersoft sets. Neutrosophic Sets Syst. 32, 294–306 (2020). https://doi.org/10.5281/zenodo.3723155

    Article  Google Scholar 

  33. Saqlain, M., Saeed, M., Ahmad, M.R., Smarandache, F.: Generalization of TOPSIS for neutrosophic hypersoft sets using accuracy function and its application. Neutrosophic Sets Syst. 27, 131–137 (2020). https://doi.org/10.5281/zenodo.3275533

    Article  Google Scholar 

  34. Sezgin, A., Atagün, A.O.: On operations of soft sets. Comput. Math. Appl. 61(5), 1457–1467 (2011). https://doi.org/10.1016/j.camwa.2011.01.018

    Article  MathSciNet  MATH  Google Scholar 

  35. Shah, N., Hussain, A.: Neutrosophic soft graphs. Neutrosophic Sets Syst. 11, 31–44 (2016). https://doi.org/10.5281/zenodo.571574

    Article  Google Scholar 

  36. Smarandache, F.: Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis and Synthetic Analysis. American Research Press, Rehoboth (1998)

    MATH  Google Scholar 

  37. Smarandache, F.: A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1999)

    MATH  Google Scholar 

  38. Smarandache, F.: Neutrosophic set, a generalization of intuitionistic fuzzy sets. Int. J. Pure Appl. Math. 24(3), 287–297 (2005)

    MathSciNet  MATH  Google Scholar 

  39. Smarandache, F.: Neutrosophic set—a generalization of intuitionistic fuzzy set. In: Granular Computing, IEEE, International Conference, GrC, Atlanta, Georgia, USA. 38-42 (2006). https://doi.org/10.1109/GRC.2006.1635754

  40. Smarandache, F.: n-Valued refined neutrosophic logic and its applications in Physics. Prog. Phys. 4, 143–146 (2013). https://doi.org/10.5281/zenodo.49149

    Article  Google Scholar 

  41. Smarandache, F.: Operators on single valued neutrosophic sets, neutrosophic undersets, and neutrosophic offsets. J. Math. Inform. 5, 63–67 (2016). https://doi.org/10.5281/zenodo.57412

    Article  Google Scholar 

  42. Smarandache, F.: Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset Similarly for Neutrosophic Over-/Under-/OffLogic, Probability, and Statistics. Pons Editions, p. 170. Pons Publishing House, Brussels, ISBN 978-1-59973-472-9 (2016). https://doi.org/10.5281/zenodo.57410

  43. Smarandache, F.: Extension of soft set of hypersoft set, and then to plithogenic hypersoft set. Neutrosophic Sets Syst. 22, 168–170 (2018). https://doi.org/10.5281/zenodo.2838716

    Article  Google Scholar 

  44. Wang, H., Rogatko, A., Smarandache, F., Sunderraman, R.: A neutrosophic description logic. In: Granular Computing, IEEE, International Conference, GrC, Atlanta, Georgia, USA, pp. 305–308 (2006). https://doi.org/10.1109/GRC.2006.1635801

  45. Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X

    Article  MATH  Google Scholar 

Download references

Funding

The authors received no specific funding for this study.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, 54000, Pakistan

    Muhammad Saeed, Atiqe Ur Rahman & Muhammad Arshad

Authors
  1. Muhammad Saeed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Atiqe Ur Rahman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Arshad
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization, M.S. and A.U.R.; methodology, M.S. and M.A.; software, A.U.R.; validation, M.S., A.U.R. and M.A.; formal analysis, M.S. and A.U.R.; investigation, A.U.R. and M.A.; visualization, M.S., A.U.R. and M.A.; supervision, M.S.; All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Atiqe Ur Rahman.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saeed, M., Rahman, A.U. & Arshad, M. A study on some operations and products of neutrosophic hypersoft graphs. J. Appl. Math. Comput. 68, 2187–2214 (2022). https://doi.org/10.1007/s12190-021-01614-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-021-01614-w

Keywords

Mathematics Subject Classification

Search

Navigation