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Kaytoue, M.; Kuznetsov, S.O.; Assaghir, Z.; Napoli, A.: Embedding tolerance relations in concept lattices : an application in information fusion (2010)
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- Abstract
- Formal Concept Analysis (FCA) is a well founded mathematical framework used for conceptual classication and knowledge management. Given a binary table describing a relation between objects and attributes, FCA consists in building a set of concepts organized by a subsumption relation within a concept lattice. Accordingly, FCA requires to transform complex data, e.g. numbers, intervals, graphs, into binary data leading to loss of information and poor interpretability of object classes. In this paper, we propose a pre-processing method producing binary data from complex data taking advantage of similarity between objects. As a result, the concept lattice is composed of classes being maximal sets of pairwise similar objects. This method is based on FCA and on a formalization of similarity as a tolerance relation (reexive and symmetric). It applies to complex object descriptions and especially here to interval data. Moreover, it can be applied to any kind of structured data for which a similarity can be dened (sequences, graphs, etc.). Finally, an application highlights that the resulting concept lattice plays an important role in information fusion problem, as illustrated with a real-world example in agronomy.
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Priss, U.: Faceted knowledge representation (1999)
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- Abstract
- Faceted Knowledge Representation provides a formalism for implementing knowledge systems. The basic notions of faceted knowledge representation are "unit", "relation", "facet" and "interpretation". Units are atomic elements and can be abstract elements or refer to external objects in an application. Relations are sequences or matrices of 0 and 1's (binary matrices). Facets are relational structures that combine units and relations. Each facet represents an aspect or viewpoint of a knowledge system. Interpretations are mappings that can be used to translate between different representations. This paper introduces the basic notions of faceted knowledge representation. The formalism is applied here to an abstract modeling of a faceted thesaurus as used in information retrieval.
- Date
- 22. 1.2016 17:30:31
-
Luksch, P.; Wille, R.: ¬A mathematical model for conceptual knowledge systems (1991)
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- Abstract
- Objects, attributes, and concepts are basic notations of conceptual knowledge; they are linked by the following four basic relations: an object has an attribute, an object belongs to a concept, an attribute abstracts from a concept, and a concept is a subconcept of another concept. These structural elements are well mathematized in formal concept analysis. Therefore, conceptual knowledge systems can be mathematically modelled in the frame of formal concept analysis. How such modelling may be performed is indicated by an example of a conceptual knowledge system. The formal definition of the model finally clarifies in which ways representation, inference, acquisition, and communication of conceptual knowledge can be mathematically treated
-
Prediger, S.: Kontextuelle Urteilslogik mit Begriffsgraphen : Ein Beitrag zur Restrukturierung der mathematischen Logik (1998)
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- Date
- 26. 2.2008 15:58:22
-
Vogt, F.; Wille, R.: TOSCANA - a graphical tool for analyzing and exploring data (1995)
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- Source
- Knowledge organization. 22(1995) no.2, S.78-81
-
Priss, U.: Faceted information representation (2000)
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- Date
- 22. 1.2016 17:47:06
