title: A lattice-theoretic approach to multigranulation approximation space.
abstract: In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators [Formula in text] forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp., union) intersection structure, if and only if the collection of multigranulation upper (lower) definable sets forms a distributive lattice when n = 2, and if and only if [Formula in text]. The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces.
authors.affiliation: College of Science, Xi'an Shiyou University, Xi'an 710065, China.
authors.forename: Xiaoli
authors.initials: X
authors.lastname: He
authors.affiliation: College of Science, Xi'an Shiyou University, Xi'an 710065, China.
authors.forename: Yanhong
authors.identifier: 0000-0001-7735-4999
authors.initials: Y
authors.lastname: She
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D016571:Neural Networks, Computer