A new soft group definition is given by Ghosh and Samanta by using the definition of soft element which is introduced by Wardowski. In this paper we study on binary operation on a soft set by using the soft element definition. Considering this binary operation which is the generalization of the soft group definition of Ghosh and Samanta we gave the notions such as soft groupoid, soft group, soft ring and some related results are obtained.
K.V.Babitha and J.J.Sunil, Soft set relations and functions, Comput Math Appl60 (2010), 1840–1849.
2.
K.V.Babitha and J.J.Sunil, Transitive closures and ordering on soft sets, Comput Math Appl62 (2011), 2235–2239.
3.
H.Aktas and N.Cagman, Soft sets and soft groups, Inform Sci177 (2007), 2726–2735.
4.
D.Molodtsov, Soft set theory-first results, Comput Math Appl37 (1999), 19–31.
5.
P.K.Maji, R.Biswas and A.R.Roy, Soft set theory, Comput Math Appl45 (2003), 555–562.
6.
D.Wardorwski, On a soft mappings and its fixed points, Fix Point Theory and Applications182 (2013).
7.
M.I.Ali, F.Feng, X.Liu, W.K.Min and M.Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications57(9) (2009), 1547–1553.
8.
D.Pei and D.Miao, From Soft Sets to Information Systems, 2005 IEEE International Conference on Granular Computing, Vol. 2, 2005, pp. 617–621. 10.1109/GRC.2005.1547365.
9.
U.Acar, F.Koyuncu and B.Tanay, Soft sets and soft rings, Comput Math Appl59 (2010), 3458–3463.
10.
J.Ghosh, D.Mandal and T.K.Samanta, Soft group based on soft element, Jordan Journal of Mathematics and Statistics (JJMS)9(2) (2016), 141–159.
11.
A.Sezgin and A.O.Atagün, Soft groups and normalistic soft groups, Comp and Math with Appl62(1) (2011), 685–698.
12.
V.Ulucay, Ö.Öztekin, M.Sahin, N.Olgun and A.Kargin, Soft representation of soft groups, New Trends in Mathematical Sciences4(2) (2016), 23–29.
13.
X.Yin and Z.Liao, Study on soft groups, Journal of Computers8(4) (2013).
