Simple proof of basic theorem for general concept lattices by cartesian representation

Authors:
Radim Belohlavek;Jan Konecny;Petr Osicka
Affiliations:
DAMOL (Data Analysis and Modeling Laboratory) Department of Computer Science, Palacký University, Olomouc, Czech Republic;DAMOL (Data Analysis and Modeling Laboratory) Department of Computer Science, Palacký University, Olomouc, Czech Republic;DAMOL (Data Analysis and Modeling Laboratory) Department of Computer Science, Palacký University, Olomouc, Czech Republic
Venue:
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
Year:
2012

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Abstract

We promote a useful representation of fuzzy sets by ordinary sets, called the Cartesian representation. In particular, we show how the main structures related to a general type of concept lattices may be reduced using this representation to their ordinary counterparts. As a consequence of this representation, we obtain a simple proof of the basic theorem for this type of concept lattices.