[1]HU Xia,FEI Peng,DU Weifeng.On collections equivalence and the granule based lower approximation operators[J].CAAI Transactions on Intelligent Systems,2018,13(2):327-330.[doi:10.11992/tis.201607018]
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On collections equivalence and the granule based lower approximation operators
CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume:
13
Number of periods:
2018 2
Page number:
327-330
Column:
学术论文—智能系统
Public date:
2018-04-15
- Title:
- On collections equivalence and the granule based lower approximation operators
- Keywords:
- approximation operators; reduct; rough sets; irreducible element; reducible element; covering; granule; collections reduct
- CLC:
- TP18
- DOI:
- 10.11992/tis.201607018
- Abstract:
- Covering based rough set is one of the methods to extend the classical rough set theory. There are three kinds of approaches, the element based definition, the granule based definition, and the subsystem based definition, to define upper and lower approximation. Most of the literature in the past tends to define based on element. In order to study the properties of the granule based approximation operators, especially the lower approximation operator, referring the concepts of irreducible element and reducible element from lattice theory, the concept of collections reduct is put forward. Starting from the concept of collections reduct, the concept and properties of collections equivalence are discussed, and collections reduction algorithm is designed. The result that collections equivalence is the necessary and sufficient condition for generating the same lower approximation by collections is given here. The preliminary theoretical preparation is done here to further develop the axiomatization of the granule based approximation operators under general binary relation.
- References:
-
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Last Update:
1900-01-01