Probabilistic graded rough set and double relative quantitative decision-theoretic rough set

• The probabilistic rough set based on coverage measure (PGRS) is proposed.
• PGRS is an extension of Pawlak's rough set and graded rough set.
• The paper proposes some rough set models, which essentially indicate the relative and absolute quantification.

The probabilistic rough set (PRS) model ignores absolute quantitative information i.e., overlap between equivalence class and basic set. And graded rough set (GRS) model cannot reflect the distinctive degrees of information. In order to overcome these defects, this paper proposes the probabilistic graded rough set (PGRS), which is an extension of Pawlak's rough set and GRS. What is more, we propose double relative quantitative decision-theoretic rough set (Drq-DTRS) models, which essentially indicate the relative and absolute quantification.