Completely lattice L-ordered sets with and without L-equality

Authors:
Pavel Martinek
Affiliations:
Department of Mathematics, Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, CZ-760 05 Zlín, Czech Republic
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

A relationship between L-order based on an L-equality and L-order based on crisp equality is explored in detail. This enables to clarify some properties of completely lattice L-ordered sets and generalize some related assertions. Namely, Belohlavek's main theorem of fuzzy concept lattices is generalized as well as his theorem dealing with Dedekind-MacNeille completion. Analogously, completion of an L-ordered set via completely lattice L-ordered set of all down-L-sets is described.