The Axiomatic Systems of Rough Fuzzy Sets on Fuzzy Approximation Spaces
Liu Gui · Chinese Journal of Computers · 2004
The theory of rough sets can be used to deal with the approximation of an arbitrary subset of a universe by two definable or observable subsets called lower and upper approximation. There are at least two methods for the development of this theory, the constructive and axiomatic approaches. The rough set axiomatic system is the foundation of rough sets theory. An advantage of the axiomatic approach is that it can focus on algebraic properties of approximation. This paper defines a pair of dual approximation operators of rough fuzzy sets and states an axiomatic system that must be satisfied by the operators. The axiomatic system of rough fuzzy sets on the fuzzy approximation space is studied. An independent axiomatic system that describes the upper approximation of the rough fuzzy sets is given. The upper approximation of the rough fuzzy sets is characterized by the axiomatic system. The axiomatic system of the upper approximation of the rough fuzzy sets also is compared with that of other rough sets.