Operations on soft sets revisited
This work solves a foundational mathematical inconsistency in soft set theory, which is incremental but important for applications in uncertainty-based fields like decision analysis.
The paper redefines intersection, complement, and difference operations for soft sets to address inconsistencies with classical set-theoretic laws, finding that the new system inherits all basic properties from classical sets.
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.