Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Modal-style operators in qualitative data analysis
ICDM '02 Proceedings of the 2002 IEEE International Conference on Data Mining
Knowledge spaces with graded knowledge states
Information Sciences: an International Journal
Isotone fuzzy Galois connections with hedges
Information Sciences: an International Journal
Closure spaces of isotone galois connections and their morphisms
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
Row and Column Spaces of Matrices over Residuated Lattices
Fundamenta Informaticae - Concept Lattices and Their Applications
Formal query systems on contexts and a representation of algebraic lattices
Information Sciences: an International Journal
On galois connections and soft computing
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advences in computational intelligence - Volume Part II
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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.