Fuzzy rough set model on two different universes and its application

The concept of the rough set was originally proposed by Pawlak as a formal tool for modeling and processing incomplete information in information systems. Then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set model on the different universe. i.e., the fuzzy rough sets model between two different universes is presented based on the fuzzy compatible relation R∼α, which is defined by a fuzzy relation R∼ between two different non-empty universes U and V and the threshold α(α ∈ (0, 1]). Several properties of this rough sets model are given, and the relationships of this model with others rough set model are examined, too. Furthermore, we also discuss two extended models of the fuzzy rough sets model based on the fuzzy rough set model on different universes. i.e., the degree fuzzy rough set and the variable precision fuzzy rough set. Meanwhile, some principal conclusions of this two rough sets model are also established. Finally, a test example is applied to interpret the background of the application and the ideals for the fuzzy rough sets model that is presented in this paper.