A Lattice-Theoretic Approach to Multigranulation Approximation Space
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-27
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
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 ( Σ i = 1 n R i ¯ , Σ i = 1 n R i _ ) 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 , Σ i = 1 n R i _ ( X ) = ∩ i = 1 n R i _ ( X ) .
The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces.
American Psychological Association (APA)
He, Xiaoli& She, Yanhong. 2014. A Lattice-Theoretic Approach to Multigranulation Approximation Space. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1051024
Modern Language Association (MLA)
He, Xiaoli& She, Yanhong. A Lattice-Theoretic Approach to Multigranulation Approximation Space. The Scientific World Journal No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-1051024
American Medical Association (AMA)
He, Xiaoli& She, Yanhong. A Lattice-Theoretic Approach to Multigranulation Approximation Space. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1051024
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1051024