Skip to main content
Log in

Fuzzy hyperstructural patterns of some genetic phenomena

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

Algebraic structures can present a suitable model of phenomena of the real world. As a result, the principles governing these structures will be useful in studying the behavior of these phenomena. In this study, we try to describe several biological phenomena in the form of fuzzy algebraic hyperstructures.

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

Access this article

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

Similar content being viewed by others

References

  • Alimov NG (1950) On ordered semigroups (Russian). Izvestiya Akad Nauk SSSR Ser Mat 14:569–576

    MathSciNet  Google Scholar 

  • Ameri R, Motameni M (2012) Fuzzy hyperideals of fuzzy hyperrings. World Appl Sci J 16(11):1604–1614

    MATH  Google Scholar 

  • Brown TA (2012) Introduction to genetics: a molecular approach. Garland Science, New York

    Book  Google Scholar 

  • Catcheside DG (1977) The genetics of recombination. University Park Press, Baltimore

    Google Scholar 

  • Chowdhury G (2009) Fuzzy transposition hypersemigroups. Iran J Fuzzy Syst 6(3):37–52

    MathSciNet  MATH  Google Scholar 

  • Chvalina J (1995) Functional graphs, quasi-ordered sets and commutative hypergroups. Masaryk University, Brno (in Czech)

  • Corsini P (1993) Prolegomena of hypergroup theory, 2nd edn. Aviani editore, Udine

    MATH  Google Scholar 

  • Corsini P, Leoreanu V (2003) Applications of hyperstructure theory, advances in mathematics. Kluwer Academic Publishers, Dordrecht

  • Davvaz B (2003) A brief survey of the theory of \(H_v\)- structures. In: Proc. 8th international congress on algebraic hyperstructures and applications, 19 Sep. 2002. Spanidis Press, Samothraki, pp 39–70

  • Davvaz B (1999) Fuzzy \(H_v\)-groups. Fuzzy Sets Syst 101:191–195

    Article  Google Scholar 

  • Davvaz B (2001) Fuzzy \(H_v\)-submodules. Fuzzy Sets Syst 117:477–484

    Article  Google Scholar 

  • Davvaz B, Cristea I (2015) Fuzzy algebraic hyperstructures, an introduction. Springer, Berlin

    Book  Google Scholar 

  • Davvaz B, Leoreanu-Fotea V (2007) Hyperring theory and applications. International Academic Press, Cambridge

    MATH  Google Scholar 

  • He P, Xin X (2011) Fuzzy hyperlattices. Comput Math Appl 62:4682–4690

    Article  MathSciNet  Google Scholar 

  • Leoreanu-Fotea V (2009) Fuzzy hypermodules. Comput Math Appl 57:466–475

    Article  MathSciNet  Google Scholar 

  • Leoreanu-Fotea V, Davvaz B (2009) Fuzzy hyperrings. Fuzzy Sets Syst 160:2366–2378

    Article  MathSciNet  Google Scholar 

  • Marty F (1934) Sur une generalization de la notion de groupe. In: 8th congress math scandenaves, Stockholm, pp 45–49

  • Mordeson JN, Malik MS (1998) Fuzzy commutative algebra. World Publ., Singapore

    Book  Google Scholar 

  • Rosenfeld A (1971) Fuzzy groups. J Math Anal Appl 35:512–517

    Article  MathSciNet  Google Scholar 

  • Sanchez R, Morgado E, Grau R (2005) Gene algebra from a genetic code algebraic structure. J Math Biol 51:431–457

    Article  MathSciNet  Google Scholar 

  • Sen MK, Ameri R, Chowdhury G (2008) Fuzzy hypersemigroups. Soft Comput 12:891–900

    Article  Google Scholar 

  • Spartalis S, Vougiouklis T (1994) The fundamental relations on \(H_v\)-rings. Riv Mat Pura Appl 13:7–20

    Google Scholar 

  • Vougiouklis T (1991) The fundamental relation in hyperrings. The general hyperfield. In: Proceedings of the fourth international congress on algebraic hyperstructures and applications (AHA 1990). World Scientific, pp 203–211

  • Vougiouklis T (1994) Hyperstructures and their representations. Hadronic Press Inc, Palm Harber

    MATH  Google Scholar 

  • Weinstein A (1936) The theory of multiple-strand crossing over. Genetics 21(3):155–199

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. Davvaz.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Communicated by Leonardo Tomazeli Duarte.

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

Mirabdollahi, H., Davvaz, B. Fuzzy hyperstructural patterns of some genetic phenomena. Comp. Appl. Math. 40, 105 (2021). https://doi.org/10.1007/s40314-021-01489-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-021-01489-4

Keywords

Mathematics Subject Classification

Navigation