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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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2008 IEEE International Conference on Granular Computing, 2008
This paper proposes a method to reduce the number of concepts still conserving their formal structure. Our main idea is first to gather objects into classes such that the members of the same class share some set of properties, and then define a kind of Galois connection via a concept of inclusion degree in order to cope, to a certain degree (denoted as
Ju-Sheng Mi, Jing Liu, Bin Xie
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This paper proposes a method to reduce the number of concepts still conserving their formal structure. Our main idea is first to gather objects into classes such that the members of the same class share some set of properties, and then define a kind of Galois connection via a concept of inclusion degree in order to cope, to a certain degree (denoted as
Ju-Sheng Mi, Jing Liu, Bin Xie
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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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Logical Precision in Concept Lattices
Journal of Logic and Computation, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Composition of concept lattices
2008 International Conference on Machine Learning and Cybernetics, 2008The theory of concept lattices is an efficient tool for knowledge discovery. The purpose of this paper is to discuss the composed lattice of two concept lattices with the same object set. We first define a pair of Galois connection between two posets obtained from two formal contexts, and discuss the properties of the Galois connection. Then, we define
null Jian-Jun Qi +2 more
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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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Concept Learning Using Vague Concept Lattice
Neural Processing Letters, 2017Recently, the theory of Formal Concept Analysis is extensively studied with bipolar fuzzy setting for adequate analysis of vagueness in fuzzy attributes via a defined sharp boundary. However, many real life data sets contain vague attributes (i.e. beautiful, bald, and tadpole) which cannot be defined through a sharp or restricted boundaries. To process
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A lattice-free concept lattice update algorithm
International Journal of General Systems, 2015Upon a change of input data, one usually wants an update of output computed from the data rather than recomputing the whole output over again. In Formal Concept Analysis, update of concept lattice of input data when introducing new objects to the data can be done by any of the so-called incremental algorithms for computing concept lattice.
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Characteristics of three-way concept lattices and three-way rough concept lattices
Knowledge-Based Systems, 2018Abstract In classical formal concept (Wille’s concept) analysis, a basic theorem about concept lattices is that every concept lattice is a complete lattice and conversely, every complete lattice is isomorphic to a concept lattice. Three-way concept analysis is an extended theory of formal concept analysis.
Huiying Yu, Qingguo Li, Mingjie Cai
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Decomposition of Relations and Concept Lattices
Fundamenta Informaticae, 2013We introduce the decomposition of an arbitrary relation into a sequential composition of three relations, viz. of a mapping with a partial order and then the transpose of a mapping. After presenting some basic properties, we investigate the specific classes of junkfree, irreducible and minimal decompositions and show that for all relations a minimal ...
Berghammer, Rudolf, Winter, Michael
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