Feature selection based on generalized variable-precision (ϑ, σ) -fuzzy granular rough set model over two universes

Fuzzy rough set theory provides us an important theoretical tool for feature selection in machine learning and pattern recognition. In this paper, based on an arbitrary fuzzy binary relation and fuzzy granules, we construct a novel fuzzy granular rough set model for feature selection of real-valued data. Firstly, we propose variable-precision (ϑ, σ) -fuzzy granular rough set model based on fuzzy granules derived from an arbitrary fuzzy binary relation. Then the properties of the newly proposed variable-precision fuzzy approximation operators and the feature selection based on this model are studied in detail. The discernibility matrix is presented and the related reduction algorithm is constructed to find the minimal fuzzy feature subsets. Thirdly, generalized fuzzy rough sets over two universes are presented and their properties are discussed. In addition, the generalized fuzzy rough sets over two universes are used to illness diagnosis. Two examples are given to show the validity of the two new models.