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 

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