Paper Info
Title
Concept lattices of isotone vs. antitone Galois connections in graded setting: Mutual reducibility revisited
Abstract
It is well known that concept lattices of isotone and antitone Galois connections induced by an ordinary binary relation and its complement are isomorphic, via a natural isomorphism mapping extents to themselves and intents to their complements. It is also known that in a fuzzy setting, this and similar kinds of reduction fail to hold. In this note, we show that when the usual notion of a complement, based on a residuum w.r.t. 0, is replaced by a new one, based on residua w.r.t. arbitrary truth degrees, the above-mentioned reduction remains valid. For ordinary relations, the new and the usual complement coincide. The result we present reveals a new, deeper root of the reduction: It is not the availability of the law of double negation but rather the fact that negations are implicitly present in the construction of concept lattices of isotone Galois connections.
Year
DOI
Venue
2012
10.1016/j.ins.2012.02.064
Inf. Sci.
Keywords
Field
DocType
mutual reducibility,residuum w,isotone galois connection,usual notion,arbitrary truth degree,residua w,above-mentioned reduction,antitone galois connection,concept lattice,ordinary binary relation,ordinary relation,graded setting,negation,fuzzy logic
Embedding problem,Galois connection,Double negation,Discrete mathematics,Negation,Binary relation,Pure mathematics,Galois group,Isomorphism,Isotone,Mathematics
Journal
Volume
ISSN
Citations 
199,
0020-0255
27
PageRank 
References 
Authors
0.95
7
2
Name
Order
Citations
PageRank
Radim Belohlavek184257.50
Jan Konecny211517.20