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Decision reducts and bireducts in a covering approximation space and their relationship to set definability

Lynn D'eer (UGent) and Chris Cornelis (UGent)
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Abstract
In this paper, we discuss the relationship between different types of reduction and set definability. We recall the definition of a decision reduct, a gamma-decision reduct, a decision bireduct and a gamma-decision bireduct in a Pawlak approximation space and the notion of set definability both in a Pawlak and a covering approximation space. We extend the notion of discernibility between objects in a Pawlak approximation space to a covering approximation space. Moreover, we introduce the definition of a decision reduct, a gamma-decision reduct, a decision bireduct and a gamma-decision bireduct in a covering approximation space. In addition, we study interrelationships between the four types of reduction, the correspondence with positive regions and the relationship to set definability in Pawlak and covering approximation spaces. (C) 2019 Elsevier Inc. All rights reserved.
Keywords
ROUGH SETS, Bireduct, Covering, Definability, Reduct, Rough sets, Semantics

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MLA
D’eer, Lynn, and Chris Cornelis. “Decision Reducts and Bireducts in a Covering Approximation Space and Their Relationship to Set Definability.” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol. 109, 2019, pp. 42–54, doi:10.1016/j.ijar.2019.03.007.
APA
D’eer, L., & Cornelis, C. (2019). Decision reducts and bireducts in a covering approximation space and their relationship to set definability. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 109, 42–54. https://doi.org/10.1016/j.ijar.2019.03.007
Chicago author-date
D’eer, Lynn, and Chris Cornelis. 2019. “Decision Reducts and Bireducts in a Covering Approximation Space and Their Relationship to Set Definability.” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 109: 42–54. https://doi.org/10.1016/j.ijar.2019.03.007.
Chicago author-date (all authors)
D’eer, Lynn, and Chris Cornelis. 2019. “Decision Reducts and Bireducts in a Covering Approximation Space and Their Relationship to Set Definability.” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 109: 42–54. doi:10.1016/j.ijar.2019.03.007.
Vancouver
1.
D’eer L, Cornelis C. Decision reducts and bireducts in a covering approximation space and their relationship to set definability. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. 2019;109:42–54.
IEEE
[1]
L. D’eer and C. Cornelis, “Decision reducts and bireducts in a covering approximation space and their relationship to set definability,” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol. 109, pp. 42–54, 2019.
@article{8698767,
  abstract     = {{In this paper, we discuss the relationship between different types of reduction and set definability. We recall the definition of a decision reduct, a gamma-decision reduct, a decision bireduct and a gamma-decision bireduct in a Pawlak approximation space and the notion of set definability both in a Pawlak and a covering approximation space. We extend the notion of discernibility between objects in a Pawlak approximation space to a covering approximation space. Moreover, we introduce the definition of a decision reduct, a gamma-decision reduct, a decision bireduct and a gamma-decision bireduct in a covering approximation space. In addition, we study interrelationships between the four types of reduction, the correspondence with positive regions and the relationship to set definability in Pawlak and covering approximation spaces. (C) 2019 Elsevier Inc. All rights reserved.}},
  author       = {{D'eer, Lynn and Cornelis, Chris}},
  issn         = {{0888-613X}},
  journal      = {{INTERNATIONAL JOURNAL OF APPROXIMATE REASONING}},
  keywords     = {{ROUGH SETS,Bireduct,Covering,Definability,Reduct,Rough sets,Semantics}},
  language     = {{eng}},
  pages        = {{42--54}},
  title        = {{Decision reducts and bireducts in a covering approximation space and their relationship to set definability}},
  url          = {{http://dx.doi.org/10.1016/j.ijar.2019.03.007}},
  volume       = {{109}},
  year         = {{2019}},
}

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