Results 171 to 180 of about 986 (204)

Relational fuzzy Galois connections

2017 Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS), 2017
We propose a suitable generalization of the notion of Galois connection whose components are fuzzy relations. We prove that the construction embeds Yao's notion of fuzzy Galois connection as a particular case. Although the natural framework for the proposed notion is that of fuzzy preposets, we also prove that it behaves properly with respect to the ...
Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego   +2 more
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Armstrong systems and Galois connections

2011 IEEE International Conference on Granular Computing, 2011
In the paper [1], it is proved that any Galois connection (f, g) on a complete lattice made an Armstrong system F (f, g) . We prove in this short note that the converse holds, that is, for a given Armstrong system R, we can make a Galois connection (φ R , ψ R ) and the original Armstrong system R is identical with the induced Armstrong system F (φR, ψR)
Michiro Kondo, Sho Soneda, Bunpei Yoshii
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Triadic fuzzy Galois connections as ordinary connections

Fuzzy Sets and Systems, 2012
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Radim Belohlávek, Petr Osicka
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Relational Galois Connections

2007
Galois connections can be defined for lattices and for ordered sets. We discuss a rather wide generalisation, which was introduced by Weiqun Xia and has been reinvented under different names: Relational Galois connections between relations. It turns out that the generalised notion is of importance for the original one and can be utilised, e.g., for ...
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Biclosed Binary Relations and Galois Connections

Order, 2001
A biclosed relation between two closure spaces \(E\) and \(E'\) is a binary relation \(R\subseteq E\times E'\) with every row of its matrix representation corresponding to a closed subset of \(E'\) and every column corresponding to a closed subset of \(E\).
Florent Domenach, Bruno Leclerc
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Galois Connections for Flow Algebras

2011
We generalise Galois connections from complete lattices to flow algebras. Flow algebras are algebraic structures that are less restrictive than idempotent semirings in that they replace distributivity with monotonicity and dispense with the annihilation property; therefore they are closer to the approach taken by Monotone Frameworks and other classical
Piotr Filipiuk, Michal Terepeta, Hanne Riis Nielson, Flemming Nielson   +3 more
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On Galois Connections and Soft Computing

2013
After recalling the different interpretations usually assigned to the term Galois connection, both in the crisp and in the fuzzy case, we survey on several of their applications in Computer Science and specifically, in Soft Computing.
Francisca García-Pardo, Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego   +3 more
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Logical Relations and Galois Connections

2002
Algebraic properties of logical relations on partially ordered sets are studied. It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higher-order type. "Theorems-for-free" is used to show that the construction ensures safe abstract interpretation of parametrically ...
Kevin Backhouse, Roland Carl Backhouse
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A Diagram of Galois Connections of Functorial Topologies

Applied Categorical Structures, 2016
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Gabriele Castellini, Stan Dziobiak
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Galois Connections and Pair Algebras

Canadian Journal of Mathematics, 1969
Unless further restricted, P, Q, and R denote arbitrary partially ordered sets whose order relations are all written “≦” .An isotone mapping ϕ: P → Q is said to be residuated if there is an isotone mapping ψ: Q → P such that(RM 1) xϕψ ≧ x for all x i n P;(RM 2) yψϕ ≦ for all y in Q.Let Q* denote the partially ordered set with order relation dual to ...
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