A comparative study of rough sets for hybrid data

To discover knowledge from hybrid data using rough sets, researchers have developed several fuzzy rough set models and a neighborhood rough set model. These models have been applied to many hybrid data processing applications for a particular purpose, thus neglecting the issue of selecting an appropriate model. To address this issue, this paper mainly concerns the relationships among these rough set models. Investigating fuzzy and neighborhood hybrid granules reveals an important relationship between these two granules. Analyzing the relationships among rough approximations of these models shows that Hu’s fuzzy rough approximations are special cases of neighborhood and Wang’s fuzzy rough approximations, respectively. Furthermore, one-to-one correspondence relationships exist between Wang’s fuzzy and neighborhood rough approximations. This study also finds that Wang’s fuzzy and neighborhood rough approximations are cut sets of Dubois’ fuzzy rough approximations and Radzikowska and Kerre’s fuzzy rough approximations, respectively.