Copyright © 2013 Ping Zhu and Qiaoyan Wen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.