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 closure operations. In particular, we prove some families to be dense in any closure operation, in which the greatest and smallest dense fami...

Full description

Saved in:
Bibliographic Details
Published inCybernetics and information technologies : CIT Vol. 22; no. 3; pp. 18 - 28
Main Authors Son, Nguyen Hoang, Demetrovics, J., Thi, Vu Duc, Thuy, Nguyen Ngoc
Format Journal Article
LanguageEnglish
Published Sciendo 01.09.2022
Subjects
Closure operation
dense family
hypergraph
minimal key
transversal hypergraph
Online AccessGet full text

Cover

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.
AbstractList 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.
Author Thi, Vu Duc
Thuy, Nguyen Ngoc
Son, Nguyen Hoang
Demetrovics, J.
Author_xml – sequence: 1
  givenname: Nguyen Hoang
  surname: Son
  fullname: Son, Nguyen Hoang
  email: nhson@hueuni.edu.vn
  organization: Faculty of Mathematics, University of Sciences, Hue University, Vietnam
– sequence: 2
  givenname: J.
  surname: Demetrovics
  fullname: Demetrovics, J.
  email: demetrovics@sztaki.mta.hu
  organization: Computer and Automation Institute Hungarian Academy of Sciences, Hungary
– sequence: 3
  givenname: Vu Duc
  surname: Thi
  fullname: Thi, Vu Duc
  email: vdthi@vnu.edu.vn
  organization: Information Technology Institute, Vietnam National University, Hanoi, Vietnam
– sequence: 4
  givenname: Nguyen Ngoc
  surname: Thuy
  fullname: Thuy, Nguyen Ngoc
  email: nnthuy.cs@hueuni.edu.vn
  organization: Faculty of Information Technology, University of Sciences, Hue University, Vietnam
BookMark eNp1kE1LAzEQhoNUsNZePe8f2JrPTRZPUq0WCr3oOUzzUVK2m5Jslf57d1sRL85l3hnmfWGeWzRqY-sQuid4RrlUDwZCV1JMaYkxFVdoTBjhJceKjP7oGzTNeYf74jUjSowRW7afLndhC12IbRF98eza7IoF7ENzGuZ5E_MxuWJ9cOl8lO_QtYcmu-lPn6CPxcv7_K1crV-X86dVaaiiXWm4YRgAW0FrEBwYsSCZrCwRghowghGhlJCsdphugKmKCeJBVKSWHghnE7S85NoIO31IYQ_ppCMEfV7EtNWQumAap83GcyIkZrYGbjEoBdJTQxxWzKlK9VmzS5ZJMefk_G8ewXogqAeCeiCoB4K94fFi-IKmc8m6bTqeeqF38Zja_u1_jJT2YNk3OwB3ew
Cites_doi 10.2478/cait-2013-0002
10.1016/S0166-218X(02)00209-3
10.1016/j.tcs.2016.11.021
10.1515/cait-2014-0001
10.1016/0898-1221(91)90227-U
10.1016/0166-218X(92)90028-9
10.2478/cait-2021-0015
10.2478/cait-2013-0058
10.1515/9783110840308-026
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.2478/cait-2022-0025
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Sciences (General)
EISSN 1314-4081
EndPage 28
ExternalDocumentID oai_doaj_org_article_cbf415703d9a4d0a88a7f2c1e083e868
10_2478_cait_2022_0025
10_2478_cait_2022_002522318
GroupedDBID 0R~
4.4
5VS
9WM
AAPBV
ABFKT
ABFLS
ACGFS
ADBBV
ADBLJ
AHGSO
ALMA_UNASSIGNED_HOLDINGS
BCNDV
E0C
EBS
GROUPED_DOAJ
HZ~
J9A
KQ8
M~E
O9-
OK1
P2P
QD8
RNS
SA.
AAYXX
CITATION
SLJYH
ID FETCH-LOGICAL-c282t-c4c30aa0d529a54a31da7376d1552cac5315885739e02ba386351fa56197fa143
IEDL.DBID DOA
ISSN 1314-4081
IngestDate Tue Oct 22 15:16:11 EDT 2024
Fri Dec 06 04:09:21 EST 2024
Fri Sep 23 02:21:56 EDT 2022
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 3
Language English
License This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
http://creativecommons.org/licenses/by-nc-nd/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c282t-c4c30aa0d529a54a31da7376d1552cac5315885739e02ba386351fa56197fa143
OpenAccessLink https://doaj.org/article/cbf415703d9a4d0a88a7f2c1e083e868
PageCount 11
ParticipantIDs doaj_primary_oai_doaj_org_article_cbf415703d9a4d0a88a7f2c1e083e868
crossref_primary_10_2478_cait_2022_0025
walterdegruyter_journals_10_2478_cait_2022_002522318
PublicationCentury 2000
PublicationDate 2022-09-01
PublicationDateYYYYMMDD 2022-09-01
PublicationDate_xml – month: 09
  year: 2022
  text: 2022-09-01
  day: 01
PublicationDecade 2020
PublicationTitle Cybernetics and information technologies : CIT
PublicationYear 2022
Publisher Sciendo
Publisher_xml – name: Sciendo
References 2024042801284222641_j_cait-2022-0025_ref_007
2024042801284222641_j_cait-2022-0025_ref_018
2024042801284222641_j_cait-2022-0025_ref_008
2024042801284222641_j_cait-2022-0025_ref_005
2024042801284222641_j_cait-2022-0025_ref_016
2024042801284222641_j_cait-2022-0025_ref_006
2024042801284222641_j_cait-2022-0025_ref_017
2024042801284222641_j_cait-2022-0025_ref_009
2024042801284222641_j_cait-2022-0025_ref_010
2024042801284222641_j_cait-2022-0025_ref_011
2024042801284222641_j_cait-2022-0025_ref_003
2024042801284222641_j_cait-2022-0025_ref_014
2024042801284222641_j_cait-2022-0025_ref_004
2024042801284222641_j_cait-2022-0025_ref_015
2024042801284222641_j_cait-2022-0025_ref_001
2024042801284222641_j_cait-2022-0025_ref_012
2024042801284222641_j_cait-2022-0025_ref_002
2024042801284222641_j_cait-2022-0025_ref_013
References_xml – ident: 2024042801284222641_j_cait-2022-0025_ref_014
  doi: 10.2478/cait-2013-0002
– ident: 2024042801284222641_j_cait-2022-0025_ref_002
– ident: 2024042801284222641_j_cait-2022-0025_ref_004
  doi: 10.1016/S0166-218X(02)00209-3
– ident: 2024042801284222641_j_cait-2022-0025_ref_005
– ident: 2024042801284222641_j_cait-2022-0025_ref_003
  doi: 10.1016/j.tcs.2016.11.021
– ident: 2024042801284222641_j_cait-2022-0025_ref_007
– ident: 2024042801284222641_j_cait-2022-0025_ref_010
  doi: 10.1515/cait-2014-0001
– ident: 2024042801284222641_j_cait-2022-0025_ref_006
  doi: 10.1016/0898-1221(91)90227-U
– ident: 2024042801284222641_j_cait-2022-0025_ref_008
  doi: 10.1016/0166-218X(92)90028-9
– ident: 2024042801284222641_j_cait-2022-0025_ref_009
– ident: 2024042801284222641_j_cait-2022-0025_ref_013
– ident: 2024042801284222641_j_cait-2022-0025_ref_012
  doi: 10.2478/cait-2021-0015
– ident: 2024042801284222641_j_cait-2022-0025_ref_016
– ident: 2024042801284222641_j_cait-2022-0025_ref_017
– ident: 2024042801284222641_j_cait-2022-0025_ref_015
– ident: 2024042801284222641_j_cait-2022-0025_ref_011
  doi: 10.2478/cait-2013-0058
– ident: 2024042801284222641_j_cait-2022-0025_ref_018
– ident: 2024042801284222641_j_cait-2022-0025_ref_001
  doi: 10.1515/9783110840308-026
SSID ssj0000493185
Score 2.2651293
Snippet 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...
SourceID doaj
crossref
walterdegruyter
SourceType Open Website
Aggregation Database
Publisher
StartPage 18
SubjectTerms Closure operation
dense family
hypergraph
minimal key
transversal hypergraph
Title Investigation of Dense Family of Closure Operations
URI http://www.degruyter.com/doi/10.2478/cait-2022-0025
https://doaj.org/article/cbf415703d9a4d0a88a7f2c1e083e868
Volume 22
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEF6kXvQg1gfWR8lBUA-hm2S32Rz7sJTi42Kht2WyuxFFktKmiP_e2WwqVRAvHhNCNnwzk_lmZ_dbQi4joIpCkPiZSqnPOMeYyzAejVYsi1KreW7nIe8fuuMpm8z4bOOoL7smzMkDO-A6Ks0wx6Bf6gSYpiAExFmoAoPcwYiu2-ZLw41i6tXxXrst2Kk0hiwWHQUvJboEll42zX_LQpVY_y7Ze68a1No8L1Yf5bohWuWZ0T7Zqwmi13Mf1iRbJj8gzToEl951rRN9c0iiDY2MIveKzBtiTWo8d5aFvR68FXYC0HucG2fo5RGZjm6fBmO_PgPBV1gMlb5iKqIAVPMwAc4gCjTE-FPQVjpNgcIQ4kLwOEoMDVOIBBKIIANkRUmcAZKhY9LIi9ycEE_HrGqicoM2SCFOFYdECHxtV9vStEWu1pjIuZO6kFgiWPSkRU9a9KRFr0X6FrKvp6xEdXUDDSdrw8m_DNci7Afgsg6f5S_DIpMJxOl_jH1Gdpwr2LVi56RRLlbmAslFmbbJdm_Yv5u0K3_6BOTKy_c
link.rule.ids 314,780,784,864,2102,27924,27925,66681,68465,76164,76165
linkProvider Directory of Open Access Journals
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwED6VdgCGivIQ5ZkBCRgiksZunLE8SoG2DBSJzbrYDkJCDWpTIf495yStAMHCmChOos--u-989meAowA95aEfuYmKPZdxTjaXkD0arVgSxFbz3M5DDobt3iO7feJPFWjN98Lkfl_n1cqzErt8uTILxZnCl4x6lbInG6mXoEYpeJtVodbpXT_cL2ZWiPPaLcGFQuMvDb9FoFyofxXq73lxWpvnyewjmxdD8xjTXYN6SQ6dTvFHDaiY8To0SvObOielRvTpBgRf9DHSsZMmziXlo8YpzrGw1xevqZ38c-7fTNHJ00147F6NLnpuef6BqygRylzFVOAhepq3IuQMA19jSA5BW9k0hYrMhwvBwyAyXivGQBB58BMkRhSFCRIR2oLqOB2bbXB0yPICKjeEf4xhrDhGQtBr29qmpU04nmMi3wqZC0npgUVPWvSkRU9a9JpwbiFbPGXlqfMb6eRZlj0mVZwQMSBnoiNk2kMhMExayjdE-IxoiyawH4DL0nSmf3yWWIwvdv7X7BCWe6NBX_Zvhne7sFIMBLtKbA-q2WRm9olWZPFBOY4-Afh0xzY
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFD7oBNEHcV5wXvsgqA_Fdk3W9FGnc942QQd7C6e5iCDr2Criv_ekraKiLz62NCl8yUm-Lyf5ArAfYaACDBPfqjTwGecUc5bi0WjFbJQ6z3O3Dnnba3UH7GrIh5VQdGdhinFfF9nK47G2xVZlFotjhU85tSgpJzdLz8Icye8Wr8HcSffivv-5qkJ81x0HLt0Zfyn4bfYpTPoXYem1SExr8zh5ecs_EqHF_NJZhqWKGHonZUvWYcaMVqBehd7UO6z8oY9WIfrijZGNvMx6Z6RFjVfeYeGe28-ZW_jz-mNTNvB0DQad84d216_uPvAViaDcV0xFAWKgeTNBzjAKNcY0GGhnmaZQUehwIXgcJSZophgJIg6hRWJDSWyRSNA61EbZyGyAp2NWJE-5IexTjFPFMRGCqm1pJ0kbcPCBiRyXFheSpIFDTzr0pENPOvQacOog-_zKWVMXL7LJo6x6ulSpJVJAA4lOkOkAhcDYNlVoiOwZ0RINYD8Al1XYTP_4LTGYUGz-r9gezN-ddeTNZe96CxbKfuA2iG1DLZ-8mB1iFHm6W3Wjd7-dxS0
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Investigation+of+Dense+Family+of+Closure+Operations&rft.jtitle=Cybernetics+and+information+technologies+%3A+CIT&rft.au=Son%2C+Nguyen+Hoang&rft.au=Demetrovics%2C+J.&rft.au=Thi%2C+Vu+Duc&rft.au=Thuy%2C+Nguyen+Ngoc&rft.date=2022-09-01&rft.pub=Sciendo&rft.eissn=1314-4081&rft.volume=22&rft.issue=3&rft.spage=18&rft.epage=28&rft_id=info:doi/10.2478%2Fcait-2022-0025&rft.externalDBID=n%2Fa&rft.externalDocID=10_2478_cait_2022_002522318
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1314-4081&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1314-4081&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1314-4081&client=summon