The optimistic multigranulation T-fuzzy rough set model was established based on multiple granulations under T-fuzzy\napproximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model in\nT-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The\noptimistic multigranulation T-fuzzy rough set model is improved deeply by investigating some further properties. And a complete\nmultigranulation T-fuzzy rough set model is constituted by addressing the pessimistic multigranulation T-fuzzy rough set. The\nfull important properties of multigranulation T-fuzzy lower and upper approximation operators are also presented. Moreover,\nrelationships between multigranulation and classical T-fuzzy rough sets have been studied carefully. From the relationships, we\ncan 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\noptimistic and pessimistic multigranulation T-fuzzy rough set models, a case is considered, which is helpful for applying these\ntheories to practical issues.
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