On transitive soft sets over semihypergroups

Document Type : Research Paper

Authors

Vali-e-Asr University

Abstract

The aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $S_{H}$ and  $T_{H},$ respectively. It is shown that $T_{H}=S_{H}$ if and only if $\beta=\beta^{*}.$ We also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.

Keywords


[1] P. Corsini,  {it Prolegomena of Hypergroup Theory}, Aviani Editore, Tricesimo, 1993.

[2] P. Corsini, and  V. Leoreanu, {it Applications of Hyperstructure Theory}, Kluwer Academical Publications, Dordrecht, 2003.
[3] B. Davvaz, V. Leoreanu-Fotea, {it Hyperring Theory and Applications}, International Academic Press, USA, 2007.
[4] F. Feng, Y.M. Li, V. Leoreanu-Fotea,  Application of level soft sets in
decision making based on interval-valued fuzzy soft sets, Computers and
Mathematics with Applications 60 (2010) 1756-1767.

[5]  F. Feng, Y.B. Jun, X.Y. Liu, L.F. Li,  An adjustable approach to fuzzy
soft set based decision making, Journal of Computational and Applied
Mathematics 234 (2010) 10-20.
[6] F. Feng, X.Y. Liu, V. Leoreanu-Fotea, Y.B. Jun,  Soft sets and soft rough
sets, Information Sciences 181 (2011) 1125-1137.
[7]  F. Feng, Y.M. Li, N. Cagman,  Generalized uni-int decision making
schemes based on choice value soft sets, European Journal of Operational
Research 220 (2012) 162-170.
[8]  D. Freni, {it Une note sur le cÂœur d'un hypergroupe et sur la cl^{o}ture transitive
$betasp ast$ de $beta$. (French) [A note on the core of a
hypergroup and the transitive closure $betasp ast$ of
$beta$]}, Riv. Mat. Pura Appl., 8 (1991) 153-156.

[9]  M. Koskas, Groupes et hypergroupes homomorphes a un
demi-hypergroupe, C. R. Acad Sc., Paris, 257 (1963), 334-337.
bibitem{4}
[10] P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision
making problem, Computers and Mathematics with Applications 44 (2002) 1077-
1083.

[11]  F. Marty, {it Sur une Generalization de la Notion de Groupe}, 8th Congress
Math. Scandenaves, Stockholm, Sweden, (1934) 45-49.
[12]  D. Molodtsov, Soft set theory first results, Comput. Math. Appl. 37 (1999) 19–31.
[13]T. Vougiouklis, {it Hyperstructures and Their Representations}, Hadronic
Press, Palm Harbor, FL, 1994.