Decomposition Theorems of Fuzzy Rough Sets

Based on the structural property of Fuzzy Rough Sets which a pair of lower and upper approximations are Fuzzy sets, and the different concepts of cut sets and decomposition theorems of Fuzzy sets are used to define the concepts of cut sets of Fuzzy Rough Sets and relevant decomposition theorems of Fuzzy Rough sets. Through the different decomposition theorems of Fuzzy sets, the different decomposition theorems of Fuzzy Rough Sets are proved. The relationship between Fuzzy Rough sets and normal sets is well explained by the decomposition theorem of Fuzzy Rough Sets. The decomposition theorem presented in this paper is very import and well applied both in theory and practice.