Results 91 to 100 of about 12,528 (136)

Fuzzy Galois Connections

Mathematical Logic Quarterly, 1999
AbstractThe concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one‐to‐one correspondence with binary fuzzy relations.
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Fuzzy Galois connections categorically

MLQ, 2010
The paper deals with closed categories over complete lattice-ordered monoids \((L, \vee, \wedge, \ast, 1)\). Covariant and contravariant fuzzy Galois connections were introduced and examined by \textit{R. Bělohlávek} [Math. Log. Q. 45, No.~4, 497--504 (1999; Zbl 0938.03079)], and \textit{G. Georgescu} and \textit{A. Popescu} [Soft Comput. 7, No.~7, 458-
Gutiérrez García, Javier, Mardones-Pérez, Iraide, de Prada Vicente, María Angeles, Zhang, Dexue   +3 more
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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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Galois Connection for Hyperclones

2010 40th IEEE International Symposium on Multiple-Valued Logic, 2010
This paper is inspired by the paper of Tarasov in which he investigates maximal partial clones on a two-element set. It happens that the approach of Tarasov can be translated into the language of hyperclone theory. He introduced a notion of quasicomposition which assigns to extended hyperoperations extension of their composition.
Hajime Machida, Jovanka Pantovic, Ivo G. Rosenberg   +2 more
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A Galois Connection

Logica Universalis, 2007
The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other.
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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 \(E\).
Domenach, Florent, Leclerc, Bruno
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Duality for Quasilattices and Galois Connections

Fundamenta Informaticae, 2017
The primary goal of the paper is to establish a duality for quasilattices. The main ingredients are duality for semilattices and their representations, the structural analysis of quasilattices as Płonka sums of lattices, and the duality for lattices developed by Hartonas and Dunn.
Romanowska, Anna B., Smith, Jonathan D. H.   +1 more
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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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Triadic fuzzy Galois connections as ordinary connections

Fuzzy Sets and Systems, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Belohlavek, Radim, Osicka, Petr
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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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