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The original rough set model is primarily concerned with the approximations of sets described by a single equivalence relation on the universe. Some further investigations generalize the classical rough set model to rough set model based on a tolerance relation. From the granular computing point of view, the classical rough set theory is based on a single granulation. For some complicated issues,...
Based on the analysis of rough set model on a tolerance relation and considering of the theory of fuzzy rough set, two types of new generalized fuzzy rough set models are constructed, which are multi-granulation fuzzy rough sets on tolerance relations. It follows the research on the properties of the lower and upper approximations of the new multi-granulation fuzzy rough set models on tolerance relations...
The extension of classical rough set model is a very hot and interesting topic. In this paper, our aim is to present the first type of graded rough set (FGRS) based on rough membership function. The concepts of k-regions, k-rough degree, etc., are proposed firstly, and some of important properties are investigated in this rough set model. Moreover, the model has the corresponding properties with classical...
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