Operations on soft sets revisited

The concept of soft sets introduced by molodtsov is a general mathematical tool for dealing with uncertainty. just as the conventional set-theoretic operations of intersection,union,complement,and difference,some corresponding operations on soft sets have been proposed. unfortunately,such operations cannot keep all classical set-theoretic laws true for soft sets. in this paper,we redefine the intersection,complement,and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. we find that the new operation system on soft sets inherits all basic properties of operations on classical sets,which justifies our definitions. © 2013 ping zhu and qiaoyan wen.