title: Further study of multigranulation T-fuzzy rough sets.
abstract: The optimistic multigranulation T-fuzzy rough set model was established based on multiple granulations under T-fuzzy approximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model in T-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The optimistic multigranulation T-fuzzy rough set model is improved deeply by investigating some further properties. And a complete multigranulation T-fuzzy rough set model is constituted by addressing the pessimistic multigranulation T-fuzzy rough set. The full important properties of multigranulation T-fuzzy lower and upper approximation operators are also presented. Moreover, relationships between multigranulation and classical T-fuzzy rough sets have been studied carefully. From the relationships, we can find that the T-fuzzy rough set model is a special instance of the two new types of models. In order to interpret and illustrate optimistic and pessimistic multigranulation T-fuzzy rough set models, a case is considered, which is helpful for applying these theories to practical issues.
authors.affiliation: School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China.
authors.forename: Wentao
authors.identifier: 0000-0002-7777-0818
authors.initials: W
authors.lastname: Li
authors.affiliation: School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China.
authors.forename: Xiaoyan
authors.initials: X
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China.
authors.forename: Wenxin
authors.initials: W
authors.lastname: Sun
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical