A multi-level conceptual data

reduction approach based on the

Lukasiewicz implication

Samir Elloumi a ,Jihad Jaam b ,Ahmed Hasnah b ,

Ali Jaoua b,*,Ibtissem Nafkha c

a

Institut Sup e rieur des Sciences Appliqu e es et de Technologie de Sousse,Tunisia b

Department of Computer Science,University of Qatar,P.O.Box 2713,Doha,Qatar c Department of Computer Science,Faculty of Sciences of Tunis,University of Manar,

Le Belvedere,1060Tunis,Tunisia

Received 8October 2002;accepted 20June 2003Abstract

Starting from fuzzy binary data represented as tables in the fuzzy relational database,in this paper,we use fuzzy formal concept analysis to reduce the tables size to only keep the minimal rows in each table,without losing knowledge (i.e.,association rules ex-tracted from reduced databases are identical at given precision level).More speci cally,we develop a fuzzy extension of a previously proposed algorithm for crisp data reduction without loss of knowledge.The fuzzy Galois connection based on the Lukasiewicz implication is mainly used in the de nition of the closure operator according to a pre-cision level,which makes data reduction sensitive to the variation of this precision level.Ó2003Published by Elsevier Inc.

Keywords:Fuzzy data reduction;Lukasiewicz implication;Fuzzy Galois connection;Precision level

*

Corresponding author.Address:Department des Sciences de l’Informatique,Universite de Tunis II/Campus University,Le Belvedere,Tunis 1060,Tunisia.

E-mail addresses:samir.elloumi@fst.rnu.tn (S.Elloumi),jihad@qu.edu.qa (J.Jaam),has-nah@qu.edu.qa (A.Hasnah),jaoua@fst.rnu.tn,jaoua@qu.edu.qa (A.Jaoua),ibtissem.naf-kha@fst.rnu.tn (I.Nafkha).

0020-0255/$-see front matter Ó2003Published by Elsevier Inc.

doi:10.1016/j.ins.2003.06.013Information Sciences 163(2004)

253–262

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