Xiaoli He

Yanhong She

The Scientific World Journal

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(Σi=1nRi¯,Σi=1nRi_)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 whenn=2, and if and only if∀X⊆U,  Σi=1nRi_(X)=∩i=1nRi_(X). The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces.</jats:p

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The Scientific World JOURNAL

A Lattice-Theoretic Approach to Multigranulation Approximation Space

http://downloads.hindawi.com/journals/tswj/2014/785932.pdf

A Lattice-Theoretic Approach to Multigranulation Approximation Space

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