On soft topological hypergroups

Document Type : Research Paper

Author

Department of Mathematics, University of Harran, P.O.Box 63200, anlurfa, Turkey

Abstract

Hyperstructure theory, initiated by Marty, is a generalization theory of classical algebraic structures, while soft set
theory is a powerful mathematical approach for modeling uncertainties and imprecision. In this study, it is aimed to
introduce the concept of soft topological hypergroups by presenting a soft approachto the concept of topological hypergroups, one of the topological algebraic hyperstructures. Also, by defining the concept of a soft topological transposition hypergroup, several special types of soft topological subhypergroups are presented, and then the
relationships between these concepts are investigated. Later on,by constructing the category CSTH of soft topological hypergroups with soft topological homomorphisms, some related characterizations are established.

Keywords

References

[1] D. A. Molodtsov, Soft set theory-First results, Comput. Math. Appl., 37(4-5) (1999), 19-31.
[2] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl., 45(4-5) (2003), 555-562.
[3] F. Marty, Sur une Generalisation de la Notion de Groupe, 8th Congress Mathematiciens Scandinaves, Stockholm, 1934, pp. 45-49.
[4] A. O. Atagun and A. Sezgin, Soft substructures of rings,  elds and modules, Comput. Math. Appl., 61 (2011), 592-601.
[5] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61(7) (2011), 1786-1799.
[6] T. Shah, S. Shaheen, Soft topological groups and rings, Ann. Fuzzy Math. Inform., 7(5)(2014), 725-743.
[7] P.K. Maji, A.R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077-1083.
[8] F. Feng, Y.B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl., 56 (2008), 2621-2628.
[9] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59(2010), 3458-3463.
[10] G, Oguz, M.H. Gursoy and I. Icen, On soft topological categories, Hacet. J. Math. Stat., 48(6)(2019), 1675-1681.
[11] S. Nazmul ,S.K. Samanta, Soft topological groups, Kochi.j.Math., 5(2010), 151-161.
[12] Y.B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56 (2008), 1408-1413.
[13] G, Oguz, I. Icen and M.H. Gursoy,Actions of soft groups,Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1)(2019), 1163-1174.
[14] A. Aygunoglu, A. Aygun, Some notes on soft topological spaces, Neural Comput. Appl., 22(1) (2012), 113-119.
[15] G. Selvachandran, A. R. Salleh,Soft hypergroups and soft hypergroup homomorphism, AIP Proceedings of the 20th National Symposium on Mathematical Sciences, 2013, pp. 821-827.
[16] P.Corsini, V. Leoreanu, Applications of Hyperstructure Theory, in: Advances in Math-ematics, vol. 5, Kluwer Academic Publishers Boston, Mass, 2003.
[17] J. Wang, M. Yin and W. Gu, Soft polygroups, Comput. Math. Appl., 62(9) (2011), 3529-3537.
[18] D. Heidari, B. Davvaz and S.M.S. Modarres, Topological hypergroups in the sense of Marty, Communications in Algebra, 42(11) (2014): 4712-4721.
[19] S.Yamak, O. Kazanci and B. Davvaz, Soft hyperstructure, Comput. Math. with Appl. 62(2) (2011), 797-803.
[20] G. Selvachandran, Introduction to the theory of soft hyperrings and soft hyperring homomorphism, JP Journal of Algebra, Number Theory and Applications, 36(3)
(2015), 279-294.
[21] O. Kazanci, S. Yilmaz, S. Yamak,Soft sets and soft BCH-algebras, Hacettepe J. Math. Statistics 39 (2010), 205-217.
[22] D. Heidari, B.Davvaz and S. M. S. Modarres, Topological polygroups, Bull. Malaysian Math. Sci. Soc., 39(2)(2016), 707-721.
Journal of Hyperstructures
Volume 9, Issue 2
December 2020
Pages 81-95

Files

Share

How to cite

Statistics