On Some Types of Covering-Based ℐ,T -Fuzzy Rough Sets and Their Applications

The notions of the fuzzy β-minimal and maximal descriptions were established by Yang et al. (Yang and Hu, 2016 and 2019). Recently, Zhang et al. (Zhang et al. 2019) presented the fuzzy covering via ℐ,T-fuzzy rough set model (FCℐTFRS), and Jiang et al. (Jiang et al., in 2019) introduced the covering through variable precision ℐ,T-fuzzy rough sets (CVPℐTFRS). To generalize these models in (Jiang et al., 2019 and Zhang et al. 2019), that is, to improve the lower approximation and reduce the upper approximation, the present paper constructs eight novel models of an FCℐTFRS based on fuzzy β-minimal (maximal) descriptions. Characterizations of these models are discussed. Further, eight types of CVPℐTFRS are introduced, and we investigate the related properties. Relationships among these models are also proposed. Finally, we illustrate the above study with a numerical example that also describes its practical application.