<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>As a basic notion in algebra, closure operations have been successfully applied to many fields of computer science. In this paper we study dense family in the closure operations. In particular, we prove some families to be dense in any closure operation, in which the greatest and smallest dense families, including the collection of the whole closed sets and the minimal generator of the closed sets, are also pointed out. More important, a necessary and sufficient condition for an arbitrary family to be dense is provided in our paper. Then we use these dense families to characterize minimal keys of the closure operation under the viewpoint of transversal hypergraphs and construct an algorithm for determining the minimal keys of a closure operation.</p>
</abstract>

As a basic notion in algebra, closure operations have been successfully applied to many fields of computer science. In this paper we study dense family in the closure operations. In particular, we prove some families to be dense in any closure operation, in which the greatest and smallest dense families, including the collection of the whole closed sets and the minimal generator of the closed sets, are also pointed out. More important, a necessary and sufficient condition for an arbitrary family to be dense is provided in our paper. Then we use these dense families to characterize minimal keys of the closure operation under the viewpoint of transversal hypergraphs and construct an algorithm for determining the minimal keys of a closure operation.

Investigation of Dense Family of Closure Operations

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Investigation of Dense Family of Closure Operations"}

As a basic notion in algebra, closure operations have been successfully applied to many fields of computer science. In this paper we study dense family in the...

Investigation of Dense Family of Closure Operations

Published Online: Sep 22, 2022

Page range: 18 - 28

Received: Feb 07, 2022

Accepted: Jun 28, 2022

DOI: https://doi.org/10.2478/cait-2022-0025

Keywords
Closure operation, dense family, minimal key, hypergraph, transversal hypergraph

© 2022 Nguyen Hoang Son et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Investigation of Dense Family of Closure Operations

Published Online: Sep 22, 2022

Page range: 18 - 28

Received: Feb 07, 2022

Accepted: Jun 28, 2022

DOI: https://doi.org/10.2478/cait-2022-0025

KeywordsClosure operation, dense family, minimal key, hypergraph, transversal hypergraph

© 2022 Nguyen Hoang Son et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Closure operation, dense family, minimal key, hypergraph, transversal hypergraph