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Representing a concept lattice by a graph
Discrete Applied Mathematics, 2004 Concept lattices (also called Galois lattices) are an ordering of the maximal rectangles defined by a binary relation. In this paper, we present a new relationship between lattices and graphs: given a binary relation R, we define an underlying graph G_R, and establish a one-to-one correspondence between the set of elements of the concept lattice of R ...
Anne Berry, Alain Sigayret
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Properties of concept lattices
1999Mathematical lattice theory classifies lattices according to their structural properties. The most important such property, namely distributivity, has already been mentioned in Section 0.3 and has been used several times since then. Now we shall examine it a little more closely. For this purpose, we concentrate on doubly founded lattices, a choice that
Bernhard Ganter, Rudolf Wille
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Covering Concept Lattices with Concept Chains
2019The total number of concepts in a concept lattice tends to grow exponentially with the size of a context. There are numerous methods for selecting a subset of concepts based on some interestingness measure. We propose a method for finding interesting concept chains instead of interesting concepts.
Ants Torim, Marko Mets, Kristo Raun
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Textural dependency and concept lattices
International Journal of Approximate Reasoning, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximations in Concept Lattices
2010Motivated by Rough Set Theory we describe an interval arithmetic on complete lattices. Lattice elements get approximated by approximations which are pairs consisting of a lower and an upper approximation. The approximations form a complete lattice again. We describe these lattices of approximations by formal contexts.
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2014
Outlier detection in mixed-type data, which contain both discrete and continuous features, is still a challenging problem. Here we newly introduce concept-based outlierness, which is defined on a hierarchy of clusters of data points and features, called the concept lattice, obtained by formal concept analysis (FCA). Intuitively, this outlierness is the
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Outlier detection in mixed-type data, which contain both discrete and continuous features, is still a challenging problem. Here we newly introduce concept-based outlierness, which is defined on a hierarchy of clusters of data points and features, called the concept lattice, obtained by formal concept analysis (FCA). Intuitively, this outlierness is the
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Subdirect decomposition of concept lattices
Algebra Universalis, 1983This paper is a continuation of a previous paper of the author where the basic theorem for ''concept lattices'' has been given [Ordered sets, Proc. NATO Adv. Study Inst., Banff/Can. 1981, 445-470 (1982; Zbl 0491.06008)]. A concept lattice can be regarded as a complete meet-sublattice of the power set lattice of ''objects'' determined by the Galois ...
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Parallel algorithms for concept lattice
2012 IEEE 10th Jubilee International Symposium on Intelligent Systems and Informatics, 2012The increasing interest on application of concept lattices in the different information systems results in several implementations and algorithm proposals and representation tools [1], [2] and [6]. The concept lattice may be used for representation of the concept generalization structure generated from the underlying data set.
József Vásárhelyi, László Kovács
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Logical Precision in Concept Lattices
Journal of Logic and Computation, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Congruence Lattices of Finite Lattices as Concept Lattices
1990In formal concept analysis it is of increasing interest to compute and to represent congruence lattices of finite lattices (for instance, to assist adequate drawings of concept lattices). In this note we give a representation of such congruence lattices as concept lattices which allows the use of developed computer programs to determine and to draw ...
Sigrid Knecht, Rudolf Wille
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