Rough Set Model Based On Random Sets And Their Applications

In this paper, the approximation operators and the random sets, the best parts of the rough sets theory, are studied systematically. The general frame of the rough sets model based on the random sets is also produced. The random sets are used to study the rough sets approximation operators, and some applications about them are produced. The mainly results and originalities are summarized as follows:Some rows equal properties about the rough approximation operators based on the random sets are produced. Under the dual relations, the approximation operators have some rows equivalent conclusions;we found the equivalent conclusions are also established under two universes of discourse and proved these equivalent conclusions in random approximation operators' concepts.The upper rough equal, the lower rough equal and rough equal are defined. Some rows correlation properties are also produced. The upper rough equal, the lower rough equal based on the random sets are used to express upper approximation operators and the lower approximation operators based on the random sets. In this article, we explained why we shouldn't simply use the sum aggregate of equivalence class to define the equivalence class of sum aggregate;and why we shouldn't use the occurs together of equivalence class to define the equivalence class of occurs together.The random rough approximation space is defined. We also proved a one-to-one correspondence between the class of the random rough sets and the random rough approximation space.The rough measure and the approximation precision in random approximation space are defined. We expounded the size of the upper (lower) approximation's cardinal number of value function with two contained relational sets;simultaneously we also expounded the size of the rough measure and theapproximation precision of value function with two contained relational sets.? The random upper (lower) approximations are defined with sum aggregate of set;the random upper (lower) approximations are also defined with sum aggregate of equivalence class. The similar nature like the upper (lower) defined by the set of points is defined.? The degree upper (lower) approximation operators are defined in this paper. Some rows degree approximation operators' natures are also produced. We pointed out that the degree approximation operators based on the random sets didn't have the natures that the lower approximation maintains occur and the upper approximation maintains sum while which have under the classic rough sets. We proved that the upper approximation's cardinal number of four Yuan foreword group A will change in a small way while the lower approximation's cardinal number will change in a big way with the increase of degree k. Simultaneously, the conclusions are produced that there is small cardinal number of the degree upper approximation based on the random sets corresponded the value function which have small cardinal number, to the contrary, there is big cardinal number of the degree lower approximation based on the random sets corresponded the value function which have small cardinal number.