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Spectral lattices of (R)over-bar(max),(+)-Formal contexts

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URI: https://hdl.handle.net/10016/8787
ISSN: 0302-9743 (Print)
ISSN: 1611-3349 (Online)
ISBN: 978-3-540-78136-3
DOI: 10.1007/978-3-540-78137-0_9
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ICFCA08-spectrum.pdf (246.95 KB)
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2008-02-15
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Springer
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Abstract
In [13] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. Subsequently, the structural lattice of such generalised contexts was introduced in [15], to provide a limited equivalent to the main theorem of K-Formal Concept Analysis, resting on a crucial parameter, the degree of existence of the object-attribute pairs phi. In this paper we introduce the spectral lattice of a concrete instance of K-Formal Concept Analysis, as a further means to clarify the structural and the K-Concept Lattices and the choice of p. Specifically, we develop techniques to obtain the join- and meet-irreducibles of a (R) over bar (max),+-Concept Lattice independently of phi and try to clarify its relation to the corresponding structural lattice.
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Proceeding of: 6th International Conference, ICFCA 2008, Montreal, Canada, February 25-28, 2008
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Spectral lattices, max-plus
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Formal Concept Analysis : 6th International Conference, ICFCA 2008, Montreal, Canada, February 25-28, 2008. Proceedings. Springer, 2008, pp. 124-139
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