The Decomposition and Representation Theorem of Rough Fuzzy Set

Abstract

In this paper, aimed at rough fuzzy sets, the concept of four kinds upper (lower) lambda- cut sets and stronger lambda-cut sets are introduced. Finally, the new operators cup,cap,c and a kind of new nested sets are put forward. Using them, the decomposition and the representation theorems are obtained. With this change, relatively less information will be lost in the decision-making process. It gives us new theoretical basis for information process.