Variable precision multi-granulation covering rough intuitionistic fuzzy sets

Since the classical Pawlak rough sets model only divides the domain by a single equivalence relation when dealing with uncertain information and ignores the influence of noisy data. In response to this problem, in this paper, we combine covering theory and intuitionistic fuzzy sets theory to propose variable precision multi-granulation covering rough intuitionistic fuzzy set (VPMCIFS) models. First, we construct eight different types of VPMCIFS models based on the minimum description and maximum description by setting two constraints (alpha, beta) in variable precision and introducing them into the multi-granulation covering rough intuitionistic fuzzy set (MCIFS) models. Moreover, we discuss the properties of these models, respectively, and analyze the relationship between the proposed models and existing models. Second, based on these models, we define the approximate accuracy of the VPMCIFS models based on the minimum description and maximum description, respectively. Finally, the validity of these models was verified by the case study of dermatosis patients, and these models were analyzed and compared. By changing the values of alpha and beta, the lower and upper approximations and approximate accuracy of each model are obtained, and the effects of different constraints on the models are analyzed and discussed. The model analyzes the problem from multiple angles and has a certain fault tolerance ability, which can effectively deal with the impact of error and noise data.