Parameter significance and reductions of soft sets

In this paper, the relationship between any two objects in a soft set is investigated in detail and a novel notion of parameter significance is introduced. Sufficient and necessary conditions on characterizing pseudo parameter reductions and normal parameter reductions with respect to the parameter significance are proposed. Two algorithms for pseudo parameter reductions and normal parameter reductions of a soft set are established. With these algorithms, all pseudo parameter reductions and all normal parameter reductions can be directly evaluated and obtained simultaneously. Several examples show the effectiveness and feasibility of the proposed approach to parameter reductions of a soft set.