Extension of HyperAlgebra to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra (Revisited)

  • Conference paper
  • First Online:
Intelligent Methods Systems and Applications in Computing, Communications and Control (ICCCC 2022)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1435))

Included in the following conference series:

  • 357 Accesses

Abstract

This is a review paper. The nth-Powerset of a Set, and the concepts built on it such as SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra are recalled and then prolonged to the Neutrosophic SuperHyperStructures {or more accurately Neutrosophic (m,n)-SuperHyperStructures}.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Marty, F.: Sur une généralisation de la Notion de Groupe. In: 8th Congress Math. Scandinaves, Stockholm, Sweden, pp. 45–49 (1934)

    Google Scholar 

  2. Smarandache, F.: SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In: Section into the Author’s Book Nidus Idearum. Scilogs, II: de rerum consectatione, 2nd edn., pp. 107–108 (2016)

    Google Scholar 

  3. Smarandache, F.: Introduction to the n-SuperHyperGraph - the most general form of graph today. In: Neutrosophic Sets and Systems, vol. 48, pp. 483–485 (2022). http://fs.unm.edu/NSS/n-SuperHyperGraph.pdf

  4. Smarandache, F.: Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-) HyperAlgebra. Neutrosophic Sets and Systems, vol. 33, pp. 290–296 (2020). https://doi.org/10.5281/zenodo.3783103. http://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf

  5. Rezaei, A., Smarandache, F., Mirvakili, S.: Applications of (neutro/anti)sophications to SemiHyperGroups. J. Math. 1–7 (2021)

    Google Scholar 

  6. Ibrahim, M.A., Agboola, A.A.A.: Introduction to NeutroHyperGroups. Neutrosophic Sets and Systems, vol. 38, pp. 15–32 (2020). https://doi.org/10.5281/zenodo.4300363. http://fs.unm.edu/NSS/IntroductionToNeutroHyperGroups2.pdf

  7. Al-Tahan, M., Davvaz, B., Smarandache, F., Anis, O.: On some NeutroHyperstructures. Symmetry 13, 535, 12 (2021). https://doi.org/10.3390/sym13040535. http://fs.unm.edu/NeutroHyperstructure.pdf

  8. Agboola, A.A.A., Davvaz, B.: On neutrosophic canonical hypergroups and neutrosophic hyperrings. In: Neutrosophic Sets and Systems, vol. 2, pp. 34–41 (2014)

    Google Scholar 

  9. Nawaz, S., Gulistan, M., Khan, S.: Weak LA-hypergroups; neutrosophy, enumeration and redox reaction. In: Neutrosophic Sets and Systems, vol. 36, pp. 352–367. https://doi.org/10.5281/zenodo.4065464

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Florentin Smarandache .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Smarandache, F. (2023). Extension of HyperAlgebra to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra (Revisited). In: Dzitac, S., Dzitac, D., Filip, F.G., Kacprzyk, J., Manolescu, MJ., Oros, H. (eds) Intelligent Methods Systems and Applications in Computing, Communications and Control. ICCCC 2022. Advances in Intelligent Systems and Computing, vol 1435. Springer, Cham. https://doi.org/10.1007/978-3-031-16684-6_36

Download citation

Publish with us

Policies and ethics

Navigation