Soft Computing

, Volume 21, Issue 19, pp 5841–5850 | Cite as

EL-hyperstructures associated to n-ary relations

Methodologies and Application

Abstract

This contribution deals with n-ary relations and hyperstructure theory. There exists a way of creating semihypergroups and hypergroups from (partially) quasi-ordered (semi)groups known as Ends lemma construction. In this paper, we use this method to introduce a new class of (semi)hypergroup from a given (semi)group endowed with a preordering n-ary relation as a generalization of EL-hyperstructures. Then, we study some basic properties and important elements belonging to this class and the essential differences between this new class and the earlier one (i.e. EL-hyperstructures) are also investigated.

Keywords

Ends lemma EL-hyperstructure (semi)hypergroup n-ary relation 

Notes

Acknowledgments

The authors are highly grateful to the referees for their valuable comments and suggestions for improving the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest in this paper.

References

  1. Anvariyeh SM, Mirvakili S, Davvaz B (2010) Pawlak’s approximations in \(\Gamma \)-semihypergroups. Comput Math Appl 60:45–63MathSciNetCrossRefMATHGoogle Scholar
  2. Bonansinga P, Corsini P (1982) On semihypergroup and hypergroup homomorphisms. Boll Union Mat Ital B 6:717–727MathSciNetGoogle Scholar
  3. Chvalina J (1995) Functional graphs, quasi-ordered sets and commutative hypergroups. Masaryk University, Brno (in Czech)Google Scholar
  4. Chvalina J, Hoškova-Mayerová S (2014) On certain proximities and preorderings on the transposition hypergroups of linear first-order partial differential operators. Anal St Univ Ovidius Constanta 22(1):85–103MathSciNetMATHGoogle Scholar
  5. Corsini P, Leoreanu V (2003) Applications of hyperstructure theory. Advances in mathematics. Kluwer Academic Publishers, DordrechtCrossRefMATHGoogle Scholar
  6. Corsini P (2003) Hyperstrutures associated with ordered sets. Bull Greek Math Soc 48:7–18MathSciNetMATHGoogle Scholar
  7. Cristea I, Stefănescu M (2009) Hypergroups and \(n\)-ary relations. Eur J Comb 31(3):780–789MathSciNetCrossRefMATHGoogle Scholar
  8. Davvaz B (2012) Polygroup theory and related system. World Scientific Publishing, SingaporeCrossRefMATHGoogle Scholar
  9. Davvaz B, Leoreanu V (2010) Binary relations on ternary semihypergroups. Commun. Algebra 38:3621–3636MathSciNetCrossRefMATHGoogle Scholar
  10. Ghazavi SH, Anvarieh SM, Mirvakili S (2015) EL\(^2\)-hyperstructures derived from (partially) quasi ordered hyperstructures. Iran J Math Sci Inf 10(2):99–114MathSciNetMATHGoogle Scholar
  11. Ghazavi SH, Anvarieh SM, Mirvakili S (2016) Ideals in EL-semihypergroups associated to ordered semigroups. J Algebraic Syst 3(2):109–125MathSciNetGoogle Scholar
  12. Gutan C (1991) Simplifiable semihypergroups. Algebraic hyperstructures and applications, (Xanthi, 1990), 103–111. World Scientific Publishing, TeaneckGoogle Scholar
  13. Hošková S (2008a) Binary hyperstructures determined by relational and transformation systems. Habilitation thesis, Faculty of Science, University of OstravaGoogle Scholar
  14. Hošková S (2008b) Order hypergroups-The unique square root condition for quasi-order hypergroups. Set Valued Math Appl 1:1–7Google Scholar
  15. Hošková S, Chvalina J (2008c) Discrete transformation hypergroups and transformation hypergroups with phase tolerance space. Discrete Math. 308(18):43–54Google Scholar
  16. Heidari D, Davvaz B (2011) On ordered hyperstructures. UPB Sci Bull Ser A 73(2):85–96MathSciNetMATHGoogle Scholar
  17. Hu J, Chen L, Qiu S, Liu M (2014) A new approach for n-ary relationships in object databases. Conceptual modeling. Springer International Publishing, New YorkGoogle Scholar
  18. Marty F (1934) Sur une generalization de la notion de groupe, In: Proceedings of 8th Congres des Mathematiciens Scandinaves, StockholmGoogle Scholar
  19. Novák M (2012) EL-hyperstructures: an overview. Ratio Math. 23:65–80Google Scholar
  20. Novák M (2011) Important elements of EL-hyperstructures. In: APLIMAT: 10th International Conference, STU in Bratislava, Bratislava, pp 151–158Google Scholar
  21. Novák M (2013) Some basic properties of EL-hyperstructure. Eur J Combin 34:446–459MathSciNetCrossRefMATHGoogle Scholar
  22. Novák M (2010) The notion of subhyperstructure of “Ends lemma”-based hyperstructures. Aplimat J Appl Math 3(II):237–247Google Scholar
  23. Novák M (2014) n-ary hyperstructures constructed from binary quasi-ordered semigroups. Anal Şt Univ Ovidius Constanta 22(3):147–168MathSciNetMATHGoogle Scholar
  24. Novák M (2015) On EL-semihypergroups. Eur J Combin Part B 44:274–286Google Scholar
  25. Račkova P (2008) Hypergroups of symmetric matrices. In: Proceedings of 10th international congress of algebraic hyperstructures and applications (AHA)Google Scholar
  26. Rosenberg IG (1998) Hypergroups and join spaces determined by relations. Ital J Pure Appl Math 4:93–101Google Scholar
  27. Vougiouklis T (1987) Generalization of P-hypergroups. Rend Circ Mat. Palermo 36(II):114–121Google Scholar
  28. Vougiouklis T (1992) Representation of hypergroups by generalized permutations. Algebra Univ 29:172–183MathSciNetCrossRefMATHGoogle Scholar
  29. Zielinsky B (2015) Generalised n-ary relations and allegories in relational and algebraic methods in computer science. Springer International Publishing, ChamGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsYazd UniversityYazdIran

Personalised recommendations