Operations on soft sets revisited by Ping Zhu and Qiaoyan Wen.
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft sets from given soft sets, some 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.
An interesting paper will get you interested in soft sets if you aren’t already.
It isn’t easy going, even with the Alice and Bob examples, which I am sure the authors found immediately intuitive.
If you have data where numeric values cannot be assigned, it will be worth your while to explore this paper and the literature on soft sets.