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A Notion of Convergence in Fuzzy Partially Ordered Sets
Mathematics, 2020 The notion of sequential convergence in fuzzy partially ordered sets, under the name oF-convergence, is well known. Our aim in this paper is to introduce and study a notion of net convergence, with respect to the fuzzy order relation, named o-convergence,
Dimitrios Georgiou +2 more
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Drawing Order Diagrams Through Two-Dimension Extension
Journal of Graph Algorithms and Applications, 2023 Ordinal real-world data such as concept hierarchies, ontologies, genealogies, or task dependencies in scheduling often has the property to not only contain pairwise comparable, but also incomparable elements.
Dominik Dürrschnabel +2 more
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Order Filter Model for Minuscule Plücker Relations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The Plücker relations which define the Grassmann manifolds as projective varieties are well known. Grass-mann manifolds are examples of minuscule flag manifolds.
David C Lax
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SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, III: THE CASE OF TOTALLY ORDERED SETS [PDF]
International Journal of Algebra and Computation, 2004 For a partially ordered set P, let Co(P) denote the lattice of all order-convex subsets of P. For a positive integer n, we denote by [Formula: see text] (resp., SUB(n)) the class of all lattices that can be embedded into a lattice of the form [Formula: see text] where <Ti|i∈I> is a family of chains (resp., chains with at most n elements).
Marina V. Semenova, Friedrich Wehrung
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Lattice structure of Grassmann-Tamari orders [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Tamari order is a central object in algebraic combinatorics and many other areas. Defined as the transitive closure of an associativity law, the Tamari order possesses a surprisingly rich structure: it is a congruence-uniform lattice.
Thomas McConville
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Mechanical characterisation of novel aperiodic lattice structures
Materials & Design, 2023 This paper compares the mechanical properties of a class of lattice metamaterials with aesthetically-pleasing patterns that are governed by the mathematics of aperiodic order.
Chikwesiri Imediegwu +5 more
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An Order-Theoretic Study on Formal Concept Analysis
Axioms, 2023 This paper employs an order-theoretic framework to explore the intricacies of formal concepts. Initially, we establish a natural correspondence among formal contexts, preorders, and the resulting partially ordered sets (posets).
Yu-Ru Syau, En-Bing Lin, Churn-Jung Liau
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A maximal chain approach to topology and order
International Journal of Mathematics and Mathematical Sciences, 1988 On ordered sets (posets, lattices) we regard topologies (or, more general convergence structures) which on any maximal chain of the ordered set induce its own interval topology.
R. Vainio
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Symmetries among Multivariate Information Measures Explored Using Möbius Operators
Entropy, 2019 Relations between common information measures include the duality relations based on Möbius inversion on lattices, which are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion).
David J. Galas, Nikita A. Sakhanenko
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices.
Křehlík Štěpán, Novák Michal
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