A novel granular variable precision fuzzy rough set model and its application in fuzzy decision system

The comparable property (or inclusion property) is the basic property of rough set theory. Unfortunately, the well-known granular variable precision fuzzy rough set does not satisfy the comparable property. To remedy this gap, a novel granular variable precision fuzzy rough set model with comparable property is proposed and discussed. Firstly, by analyzing the existing granular precision fuzzy rough set models, we find the reason that they do not satisfy the comparable property. Then, we give a new granular precision fuzzy rough set model with the comparable property. Secondly, we study the basic properties, characterization theorem and accuracy measure of the new model. Thirdly, we apply the novel model in the study of fuzzy decision system. An attribute reduction method is developed, and the corresponding attribute reduction algorithm is designed. Finally, by using public accessible datasets, we make a series of experiments to verify the effectiveness and reliability of our method and make comparisons with some existing attribute reduction methods.