Variable precision rough fuzzy set model based on general relations

In order to effectively handle the real-valued data sets in practice, it is valuable from theoretical and practical aspects to combine fuzzy rough set (FRS) and variable precision rough set (VPRS) so that a powerful tool can be developed. That is, the model of fuzzy variable precision rough set (FVPRS), which not only can handle numerical data but also is less sensitive to misclassification and perturbation,In this paper, we propose a new variable precision rough fuzzy set by introducing the variable precision parameter to generalized rough fuzzy set, i.e., the variable precision rough fuzzy set based on general relation. We define the lower and upper approximations of any fuzzy set with variable precision parameter by constructive approach. Then we establish the relation between the model proposed in this paper and the existing models. Finally, we present the properties of the proposed model in detail. The results enrich the theory and also extend the application fields for rough set theory.