This paper studies -fuzzy multigranulation rough set based on residuted lattices, which is considered as an extension of the classical -fuzzy rough set. Two models of -fuzzy optimistic multigrannulation rough set and -fuzzy pessimistic multigrannulation rough set based on residuted latteices are suggested. Then, we mainly investigate some fundamental properties of the -fuzzy multigranulation rough set model. With regards to residuated lattices’ topology, we study the topological and the lattice structure in the -fuzzy optimistic multigranulation rough set model and -fuzzy pessimistic multigranulation rough set model, respectively.
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