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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

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.

References

    [1]  Belohlavek R. Similarity relations in concept lattices. J. Logic Comput. (2000) 10(6):823–845.[Abstract/Free Full Text]

    [2]  Belohlavek R. Fuzzy Relational Systems, Foundations and Principles (2002) New York: Kluwer.

    [3]  Belohlavek R, Dvorak J, Outrata J. Fast factorization by similarity in formal concept analysis of data with fuzzy attributes. J. Comput. Syst. Sci. (2007) 73(6):1012–1022.[CrossRef]

    [4]  Belohlavek R, Outrata J, Vychodil V. Thresholds and shifted attributes in formal concept analysis of data with fuzzy attributes. In: Lecture Notes in Artificial Intelligence—Schärfe H, Hitzler P, Øhrstrøm P, eds. (2006) 4068. Berlin/Heidelberg: Springer. 117–130.[CrossRef]

    [5]  Belohlavek R, Krupka M. On approximate minimization of fuzzy automata. In: Journal of Multiple–Valued Logic and Soft Computing. To appear.

    [6]  Chajda I. Algebraic Theory of Tolerance Relations (1991) Olomouc: Palacky University Press.

    [7]  Czédli G. Factor lattices by tolerances. Acta Sci. Math. (1982) 44:35–42.

    [8]  Hájek P. Metamathematics of Fuzzy Logic (1998) Dordrecht: Kluwer.

    [9]  Pogonowski J. Tolerance Spaces with Applications in Linguistics (1981) Poznan: Poznan University Press.

    [10]  Wille R. Complete tolerance relations of concept lattices. In: Contributions to General Algebra—Eigenthaler G, et al, eds. (1985) 3. Wien: Hölder-Pichler-Tempsky. 397–415.


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This Article
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Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
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