Abstract
The rough approximations on a complete completely distributive lattice L based on binary relation were introduced by Zhou and Hu (Inf Sci 269:378–387, 2014), where the binary relation was defined on the set of non-zero join-irreducible elements. This paper extends Zhou and Hu’s rough set model by defining new approximation operators via ideal. When I is the least ideal of L and R is a reflexive binary relation, these two approximations coincide. We present the essential properties of new approximations and also discuss how the new one relates to the old one. Finally, the topological and lattice structures of the approximations are given.
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Acknowledgments
We would like to thank the anonymous referees for their professional comments for improving the paper. This work is supported by the National Natural Science Foundation of China (Nos. 11371130, 11401195), Research Fund for the Doctoral Program of Higher Education of China (No. 20120161110017), and Hunan Provincial Natural Science Foundation of China (No. 2015JJ3050).
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Han, H., Li, Q. & Guo , L. Rough approximations via ideal on a complete completely distributive lattice. Soft Comput 20, 1853–1861 (2016). https://doi.org/10.1007/s00500-015-1873-4
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DOI: https://doi.org/10.1007/s00500-015-1873-4