Investigations on Some Operations of Soft Sets

Soft set theory was initiated by Molodtsov in 1999. In the past years, this theory had been applied to many branches of mathematics, information science and computer science. In 2003, Maji et al. introduced some operations of soft sets and gave some operational rules. Recently, some of these operational rules are pointed out to be not true. Furthermore, Ali et al., in their paper, introduced and discussed some new operations of soft sets. In this paper, we further investigate these operational rules given by Maji et al. and Ali et al.. We obtain some sufficient-necessary conditions such that corresponding operational rules hold and give correct forms for some operational rules. These results will be help for us to use rightly operational rules of soft sets in research and application of soft set theory.

• Xun Ge
• Songlin Yang

• Soft sets
• union
• intersection
• complement.

[1] H.Aktas and N.Cagman, Soft sets and soft groups, Information Sciences,
177(2007) 2726-2735.
[2] M.I.Ali, F.Feng, X.Liu, W.K.Minc and M.Shabir, On some new operations
in soft set theory, Computers & Mathematics with Applications, 57(2009),
1547-1553.
[3] F.Feng, Y.B.Jun, X.Liu, L.Li, An adjustable approach to fuzzy soft set
based decision making, Journal of Computational and Applied Mathematics,
234(2010), 10-20.
[4] X.Ge, Z.Li and Y.Ge, Topological spaces and soft sets, Journal of
Computational Analysis and Applications. In Press.
[5] Y.B.Jun and C.Hwan, ParkApplications of soft sets in ideal theory of
BCK/BCI-algebras, Information Sciences, 178(2008), 2466-2475.
[6] Z.Kong, L.Gao and L.Wang, Comment on "A fuzzy soft set theoretic
approach to decision making problems" Journal of Computational and
Applied Mathematics, 223(2009), 540-542.
[7] P.K.Maji, R.Biswas and A.R.Roy, Soft set theory, Computers & Mathematics
with Applications, 45(2003), 555-562.
[8] D.Molodtsov, Soft set theory-First results, Computers & Mathematics
with Applications, 37(1999), 19-31.
[9] K.Qin and Z.Hong, On soft equality, Journal of Computational and
Applied Mathematics. In Press.
[10] A.R.Roy, P.K.Maji, A fuzzy soft set theoretic approach to decision
making problems, Journal of Computational and Applied Mathematics,
203(2007), 412-418.
[11] Z.Xiao, K.Gong and Y.Zou, A combined forecasting approach based
on fuzzy soft sets, Journal of Computational and Applied Mathematics,
228(2009), 326-333.
[12] C.F.Yang, A note on soft set theory, Computers & Mathematics with
Applications, 56(2008) 1899-1900.
[13] Y.Zou and Z.Xiao, Data analysis approaches of soft sets under incomplete
information, Knowledge-Based Systems, 21(2008), 941-945.