Multi-Granularity Intuitionistic Fuzzy Cover Rough Sets

In order to better describe the object concept in the intuitionistic fuzzy environment and take into account the difference of fault tolerance of different objects,this paper studies the threshold of the intuitionistic fuzzy neighborhood and related upper and lower approximation operators,discusses intuitionistic fuzzy β neighborhood,intuitionistic fuzzy β covering rough set,multi-granularity intuitionistic fuzzy β degree covering rough set,correlation uncertainty measurement and attribute reduction.On the one hand,the threshold value β of the intuitionistic fuzzy neighborhood is generalized as a vector β,and the intuitionistic fuzzy vector β covering is defined.On this basis,the upper and lower approximation operators are modeled by constructing the Lukasiewicz triangle.The intuitionistic fuzzy β covering L-1 rough set and intuitionistic fuzzy vector β covering L-2 rough set are proposed,their measures are discussed,and the related reduction algorithm is designed.On the other hand,the threshold β of intuitionistic fuzzy neighborhood is generalized to β degree,and the intuitionistic fuzzy β degree covering rough set is defined.On this basis,it is extended to Multi-granulation intuitionistic fuzzy β degree covering rough set.Then,the Multi-granulation intuitionistic β fuzzy degree covering L rough set is proposed by using the Lukasiewicz triangle module,and the related properties and examples are given to verify the model’s effectiveness.The results show that the intuitionistic fuzzy β covering rough set L-1 has higher similarity with the object concept.The intuitionistic fuzzy vector,β covering L-2 rough sets have higher accuracy to some extent.The intuitionistic fuzzy β degree covering rough set preserves more useful data to a greater extent and has stronger practicability.The multi-granulation intuitionistic fuzzy β degree covering L rough set breaks through the limitation that the lower approximation of the multi-granulation intuitionistic fuzzy covering rough set is not included in the upper approximation,and the target concept is not included.