A Lattice-Theoretic Approach to Multigranulation Approximation Space
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 onl...
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/785932 |
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| author | Xiaoli He Yanhong She |
| author_facet | Xiaoli He Yanhong She |
| author_sort | Xiaoli He |
| collection | DOAJ |
| description | 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 when n=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. |
| format | Article |
| id | doaj-art-cfa8e0dfe43f48d1b568ff8b310e5af0 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
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| series | The Scientific World Journal |
| spelling | doaj-art-cfa8e0dfe43f48d1b568ff8b310e5af02025-02-03T01:10:48ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/785932785932A Lattice-Theoretic Approach to Multigranulation Approximation SpaceXiaoli He0Yanhong She1College of Science, Xi’an Shiyou University, Xi’an 710065, ChinaCollege of Science, Xi’an Shiyou University, Xi’an 710065, ChinaIn 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 when n=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.http://dx.doi.org/10.1155/2014/785932 |
| spellingShingle | Xiaoli He Yanhong She A Lattice-Theoretic Approach to Multigranulation Approximation Space The Scientific World Journal |
| title | A Lattice-Theoretic Approach to Multigranulation Approximation Space |
| title_full | A Lattice-Theoretic Approach to Multigranulation Approximation Space |
| title_fullStr | A Lattice-Theoretic Approach to Multigranulation Approximation Space |
| title_full_unstemmed | A Lattice-Theoretic Approach to Multigranulation Approximation Space |
| title_short | A Lattice-Theoretic Approach to Multigranulation Approximation Space |
| title_sort | lattice theoretic approach to multigranulation approximation space |
| url | http://dx.doi.org/10.1155/2014/785932 |
| work_keys_str_mv | AT xiaolihe alatticetheoreticapproachtomultigranulationapproximationspace AT yanhongshe alatticetheoreticapproachtomultigranulationapproximationspace AT xiaolihe latticetheoreticapproachtomultigranulationapproximationspace AT yanhongshe latticetheoreticapproachtomultigranulationapproximationspace |