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The approximations in rough concept lattice and approximable concept lattice
Journal of Intelligent & Fuzzy Systems, 2017In a formal context, the lower and upper approximations of an arbitrary set of objects are constructed by object-oriented concepts, attribute-oriented concepts, approximable concepts and weak approximable concepts, respectively. We first define the concept of approximations based on lattice-theoretic operators, and the properties of them are discussed.
Qimei Xiao +3 more
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Constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges
Fuzzy Sets and Systems, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L'ubomír Antoni +2 more
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Logic Journal of the IGPL, 2005
Summary: We describe a new approach to fuzzify a concept lattice and we show that it is a generalization and common platform for already known approaches: the classical crisp Ganter \& Wille [\textit{B. Ganter} and \textit{R. Wille}, Formal concept analysis. Berlin: Springer (1999; Zbl 0909.06001)] case, the fuzzy Pollandt [\textit{S. Pollandt}, in: G.
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Summary: We describe a new approach to fuzzify a concept lattice and we show that it is a generalization and common platform for already known approaches: the classical crisp Ganter \& Wille [\textit{B. Ganter} and \textit{R. Wille}, Formal concept analysis. Berlin: Springer (1999; Zbl 0909.06001)] case, the fuzzy Pollandt [\textit{S. Pollandt}, in: G.
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Concept Approximation in Concept Lattice
2007In this paper we present a novel approach to the concept approximations in concept lattice. Using the similar idea of rough set theory and unique properties of concept lattice, upper and lower approximations of any object or attribute set can be found by exploiting meet-(union-)irreducible elements in concept lattice, the approximations can be ...
Keyun Hu +4 more
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Decompositions of Concept Lattices
1999A complex concept lattice can possibly be split up into simpler parts. Here the mathematical model must prove its worth by providing efficacious and versatile methods for the decomposition. Every such decomposition principle can be reversed to make a construction method.
Bernhard Ganter, Rudolf Wille
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CHARACTERIZING TREES IN CONCEPT LATTICES
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2008Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree.
Radim Belohlávek +3 more
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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 ...
Rudolf Berghammer, Michael Winter 0001
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Concept Lattices of Subcontexts of a Context
Fundamenta Informaticae, 2009As an effective tool for data analysis and knowledge processing, the theory of concept lattices has been studied extensively and applied to various fields. In order to discover useful knowledge, one often ignores some attributes according to a particular purpose and merely considers the subcontexts of a rather complex context.
Xia Wang, Wenxiu Zhang
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Constructions of concept lattices
1999A construction method by means of which we obtain from two contexts K1 and K2 a new context, let us say K, can only be a useful construction principle for concept lattices, if it is invariant under reduction. This means that, if the same construction is applied to contexts whose concept lattices are isomorphic to those of K1 and K2, then the concept ...
Bernhard Ganter, Rudolf Wille
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2007
The paper presents theorems characterizing concept lattices which happen to be trees after removing the bottom element. Concept lattices are the clustering/classification systems provided as an output of formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree.
Radim Belohlávek +3 more
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The paper presents theorems characterizing concept lattices which happen to be trees after removing the bottom element. Concept lattices are the clustering/classification systems provided as an output of formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree.
Radim Belohlávek +3 more
openaire +1 more source