Let $S$ be a positive linear operator from Riesz space into a Dedekind complete one. In this paper, we introduce some subsets $\mathcal{P}_S$,$\mathcal{C}_S$ , $\mathcal{I}_S$ and $\mathcal{H}_S$ of linear operators which determined by $S$, and consider the relationship between them. And we characterize the operator $S$ in terms of above subsets of operators.