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Logic Journal of IGPL Advance Access originally published online on March 12, 2009
Logic Journal of IGPL 2009 17(2):205-223; doi:10.1093/jigpal/jzp004
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Factorization of residuated lattices

Michal Krupka

Dept. Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00, Olomouc, Czech Republic.
E-mail: michal.krupka{at}upol.cz


  Abstract

We discuss the problem of factorization of residuated lattices by similarity relations. As the main result, we introduce a natural structure of residuated lattice on factorized residuated lattice. Some consequences are also discussed: the problem of representatives and factor projections, sequential factorization, application to fuzzy sets, application to factorization of concept lattices of data with fuzzy attributes.

Key Words: Fuzzy logic • Factorization • Residuated lattice • Similarity • Concept lattice

Received for publication 4 June 2008.
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