Variable Precision Fuzzy Rough Sets

In this paper the variable precision fuzzy rough sets (VPFRS) concept will be considered. The notions of the fuzzy inclusion set and the α-inclusion error based on the residual implicators will be introduced. The level of misclassification will be expressed by means of α-cuts of the fuzzy inclusion set. Next, the use of the mean fuzzy rough approximations will be postulated and discussed. The concept of VPFRS will be defined using the extended version of the variable precision rough sets (VPRS) model, which utilises a general allowance for levels of misclassification expressed by two parameters: lower (l) and upper (u) limit. Remarks concerning the variable precision rough fuzzy sets (VPRFS) idea will be given. An example will illustrate the proposed VPFRS model.