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Treillis de Galois pour les contextes multi-valués flous. Application à l'étude des traits de vie en hydrobiologie.

Abstract : This computer information science PhD takes place in the framework of Formal Concept Analysis (FCA) or Galois lattices, which are tools based on mathematical operators called Galois connections allowing to generate concepts. A concept is composed with a set of objects sharing a set of attributes. These concepts are generated from a context which is a table of binary relations between these objects and these attributes. We are interested in complex contexts for which the complexity is based on two elements. On one hand, on many-valued context for which the attributes are divided into several modalities. On the other hand, it is based on fuzzy contexts for which the relation between objects and attributes is not binary. We define fuzzy many-valued contexts which inherit of both complexities and introduce two conversions for fuzzy many-valued data. The first conversion is a binarisation by a complete disjonctive operation allowing to use tools such as implications and to compare and combine lattices with statistical methods such as factorial analysis. The second conversion is issued from histogram scaling which we define and which converts attributes into histograms. To generate concepts from histograms, we propose new Galois connections based on a similarity measure between these histograms. These connections allow to obtain concepts where objects share attributes which are not equal but similar between the same minimum and maximum. We also propose to use thresholds to limit the number of generated concepts and decrease calculating time. We have tested and compared the performance of two algorithms : MinMaxNC and MinMaxC implementing this connection. This PhD is applied to the hydrobiological domain for which it is needed to select ecological traits allowing to caracterize ecological quality of water surfaces due to the behaviour of species in their environment. The selection of these traits is based on the search of groups of taxons sharing morphological and physiological (called biological traits) characteristics. These groups correspond to concepts in FCA and biological data can be considered as fuzzy many-valued context for which we show the efficency of our approach.
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https://tel.archives-ouvertes.fr/tel-00545647
Contributor : Aurélie Bertaux <>
Submitted on : Friday, December 10, 2010 - 7:37:44 PM
Last modification on : Friday, October 23, 2020 - 4:38:40 PM
Long-term archiving on: : Friday, March 11, 2011 - 4:10:04 AM

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  • HAL Id : tel-00545647, version 1

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Aurélie Bertaux. Treillis de Galois pour les contextes multi-valués flous. Application à l'étude des traits de vie en hydrobiologie.. Interface homme-machine [cs.HC]. Université de Strasbourg, 2010. Français. ⟨tel-00545647⟩

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