Affiliations: School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, P.R. China | School of Management, Xi'an Jiaotong University, Xi'an, P.R. China
Note: [] Corresponding author. Weihua Xu, School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, P.R. China; School of Management, Xi'an Jiaotong University, Xi'an 700049, P.R. China. E-mail: [email protected]
Abstract: Based on analysis of Pawlak's rough set model in the view of single equivalence relation and the theory of fuzzy set, associated with multi-granulation rough set models proposed by Qian, two types of new rough set models are constructed, which are multi-granulation fuzzy rough sets. It follows the research on the properties of the lower and upper approximations of the new multi-granulation fuzzy rough set models. Then it can be found that the Pawlak rough set model, fuzzy rough set model and multi-granulation rough set models are special cases of the new one from the perspective of the considered concepts and granular computing. The notion of rough measure and (α, β)-rough measure which are used to measure uncertainty in multi-granulation fuzzy rough sets are introduced and some basic properties of the measures are examined. The construction of the multi-granulation fuzzy rough set model is a meaningful contribution in the view of the generalization of the classical rough set model.
