Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators

For interval-valued fuzzy datasets, people have started to do research on interval-valued fuzzy rough sets and relevant models. However, these models could not be effectively applied to handle the real-valued datasets such as interval-valued fuzzy datasets as variable precision problems were not considered in interval-valued fuzzy rough sets. In this paper, fuzzy variable precision rough sets are generalized to interval-valued fuzzy sets, with consideration of interval precisions and interval-valued fuzzy relations. Combining interval-valued fuzzy set with rough sets and variable precision rough sets, this paper develops generalized interval-valued fuzzy variable precision rough sets (GIVF-VPRSs) based on triangular norms and fuzzy logical operators respectively. using the basic properties of GIVF-VPRSs, this paper gives granule representation form of the upper approximation operator in GIVF-VPRSs based on triangular norms and granule representation form of the lower approximation operator in GIVF-VPRSs, which is based on fuzzy logical operators. The conclusions show that some existing models, such as interval-valued fuzzy rough sets, variable precision rough sets and fuzzy variable precision rough sets, are special examples of GIVF-VPRSs proposed in this paper.