Notes on “Vague soft sets and their properties”

In this paper, we point out by counterexamples that several assertions in Xu et al. [W. Xu, J. Ma, S.Y. Wang, G. Hao, Vague soft sets and their properties, Comput. Math. Appl. 2010 (59) 787–794] are not true in general, and propose reasonable definitions to improve the results.