Uncertainty measures in multigranulation with different grades rough set based on dominance relation

The graded rough set and multi-granulation rough set are two significant generalized rough set models which be constructed on the indiscernibility relation. They solve the issues that the degree of overlap between the equivalence class and basic set in different view points of quantitative information. The purpose of this study is that research the good points of graded rough set in the multi-granulation environment which in different granules have different grades based on dominance relation. Three new types of multi-granulation with different grades rough set models are proposed, which include the optimistic, pessimistic and mean multi-granulation with different grades rough set. Then, their principal structure, basic properties and serval kinds of uncertainty measure methods are investigated as well. Furthermore, an experimental evaluation about urban investment is utilized to verify the proposed properties, which is valuable for applying these theories to deal with practical issues.