Description logics knowledge bases are a popular approach to represent terminological and assertional knowledge suitable for computers to work with. Despite that, the practicality of description logics is impaired by the difficulties one has to overcome to construct such knowledge bases. Previous work has addressed this issue by providing methods to learn valid terminological knowledge from data, making use of ideas from formal concept analysis. A basic assumption here is that the data is free of errors, an assumption that can in general not be made for practical applications. This thesis presents extensions of these results that allow to handle errors in the data. For this, knowledge that is "almost valid" in the data is retrieved, where the notion of "almost valid" is formalized using the notion of confidence from data mining. This thesis presents two algorithms which achieve this retrieval. The first algorithm just extracts all almost valid knowledge from the data, while the second algorithm utilizes expert interaction to distinguish errors from rare but valid counterexamples.

With the growing number of large data sets, the necessity of complexity reduction applies today more than ever before. Moreover, some data may also be vague or uncertain. Thus, whenever we have an instrument for data analysis, the questions of how to apply complexity reduction methods and how to treat fuzzy data arise rather naturally. In this thesis, we discuss these issues for the very successful data analysis tool Formal Concept Analysis. In fact, we propose different methods for complexity reduction based on qualitative analyses, and we elaborate on various methods for handling fuzzy data. These two topics split the thesis into two parts. Data reduction is mainly dealt with in the first part of the thesis, whereas we focus on fuzzy data in the second part. Although each chapter may be read almost on its own, each one builds on and uses results from its predecessors. The main crosslink between the chapters is given by the reduction methods and fuzzy data. In particular, we will also discuss complexity reduction methods for fuzzy data, combining the two issues that motivate this thesis. / Komplexitätsreduktion ist eines der wichtigsten Verfahren in der Datenanalyse. Mit ständig wachsenden Datensätzen gilt dies heute mehr denn je. In vielen Gebieten stößt man zudem auf vage und ungewisse Daten. Wann immer man ein Instrument zur Datenanalyse hat, stellen sich daher die folgenden zwei Fragen auf eine natürliche Weise: Wie kann man im Rahmen der Analyse die Variablenanzahl verkleinern, und wie kann man Fuzzy-Daten bearbeiten? In dieser Arbeit versuchen wir die eben genannten Fragen für die Formale Begriffsanalyse zu beantworten. Genauer gesagt, erarbeiten wir verschiedene Methoden zur Komplexitätsreduktion qualitativer Daten und entwickeln diverse Verfahren für die Bearbeitung von Fuzzy-Datensätzen. Basierend auf diesen beiden Themen gliedert sich die Arbeit in zwei Teile. Im ersten Teil liegt der Schwerpunkt auf der Komplexitätsreduktion, während sich der zweite Teil der Verarbeitung von Fuzzy-Daten widmet. Die verschiedenen Kapitel sind dabei durch die beiden Themen verbunden. So werden insbesondere auch Methoden für die Komplexitätsreduktion von Fuzzy-Datensätzen entwickelt.

We present a methodology for improving the detection of outlying Fire Service’s reports based on domain knowledge and dialogue with Fire & Rescue domain experts. The outlying report is considered as element which is significantly different from the remaining data. Outliers are defined and searched on the basis of domain knowledge and dialogue with experts. We face the problem of reducing high data dimensionality without loosing specificity and real complexity of reported incidents. We solve this problem by introducing a knowledge based generalization level intermediating between analysed data and experts domain knowledge. In the methodology we use the Formal Concept Analysis methods for both generation appropriate categories from data and as tools supporting communication with domain experts. We conducted two experiments in finding two types of outliers in which outliers detection was supported by domain experts.

We introduce a new software system called Formal Concept Analysis Research Toolbox (FCART). Our goal is to create a universal integrated environment for knowledge and data engineers. FCART is constructed upon an iterative data analysis methodology and provides a built-in set of research tools based on Formal Concept Analysis techniques for working with object-attribute data representations. The provided toolset allows for the fast integration of extensions on several levels: from internal scripts to plugins. FCART was successfully applied in several data mining and knowledge discovery tasks. Examples of applying the system in medicine and criminal investigations are considered.

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We propose an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the assertional part and by a domain expert. The use of techniques from Formal Concept Analysis ensures that, on the one hand, the interaction with the expert is kept to a minimum, and, on the other hand, we can show that the extended knowledge base is complete in a certain sense.

Formal Concept Analysis (FCA) can be used to analyze data given in the form of a formal context. In particular, FCA provides efficient algorithms for computing a minimal basis of the implications holding in the context. In this paper, we extend classical FCA by considering data that are represented by relational structures rather than formal contexts, and by replacing atomic attributes by complex formulae defined in some logic. After generalizing some of the FCA theory to this more general form of contexts, we instantiate the general framework with attributes defined in the Description Logic (DL) EL, and with relational structures over a signature of unary and binary predicates, i.e., models for EL. In this setting, an implication corresponds to a so-called general concept inclusion axiom (GCI) in EL. The main technical result of this report is that, in EL, for any finite model there is a finite set of implications (GCIs) holding in this model from which all implications (GCIs) holding in the model follow.

We present a general form of attribute exploration, a knowledge completion algorithm from formal concept analysis. The aim of this generalization is to extend the applicability of attribute exploration by a general description. Additionally, this may also allow for viewing different existing variants of attribute exploration as instances of a general form, as for example exploration on partial contexts.

Within formal concept analysis, attribute exploration is a powerful tool to semiautomatically check data for completeness with respect to a given domain. However, the classical formulation of attribute exploration does not take into account possible errors which are present in the initial data. We present in this work a generalization of attribute exploration based on the notion of confidence, which will allow for the exploration of implications which are not necessarily valid in the initial data, but instead enjoy a minimal confidence therein.

La fusion d'informations consiste à résumer plusieurs informations provenant des différentes sources en une information exploitable et utile pour l'utilisateur.Le problème de la fusion est délicat surtout quand les informations délivrées sont incohérentes et hétérogènes. Les résultats de la fusion ne sont pas souvent exploitable et utilisables pour prendre une décision, quand ils sont imprécis. C'est généralement due au fait que les informations sont incohérentes. Plusieurs méthodes de fusion sont proposées pour combiner les informations imparfaites et elles appliquent l'opérateur de fusion sur l'ensemble de toutes les sources et considèrent le résultat tel qu'il est. Dans ce travail, nous proposons une méthode de fusion fondée sur l'Analyse Formelle de Concepts, en particulier son extension pour les données numériques : les structures de patrons. Cette méthode permet d'associer chaque sous-ensemble de sources avec son résultat de fusion. Toutefois l'opérateur de fusion est choisi, alors un treillis de concept est construit. Ce treillis fournit une classification intéressante des sources et leurs résultats de fusion. De plus, le treillis garde l'origine de l'information. Quand le résultat global de la fusion est imprécis, la méthode permet à l'utilisateur d'identifier les sous-ensemble maximaux de sources qui supportent une bonne décision. La méthode fournit une vue structurée de la fusion globale appliquée à l'ensemble de toutes les sources et des résultats partiels de la fusion marqués d'un sous-ensemble de sources. Dans ce travail, nous avons considéré les informations numériques représentées dans le cadre de la théorie des possibilités et nous avons utilisé trois sortes d'opérateurs pour construire le treillis de concepts. Une application dans le monde agricole, où la question de l'expert est d'estimer des valeurs des caractéristiques de pesticide provenant de plusieurs sources, pour calculer des indices environnementaux est détaillée pour évaluer la méthode de fusion proposée / Merging pieces of information into an interpretable and useful format is a tricky task even when an information fusion method is chosen. Fusion results may not be in suitable form for being used in decision analysis. This is generally due to the fact that information sources are heterogeneous and provide inconsistent information, which may lead to imprecise results. Several fusion operators have been proposed for combining uncertain information and they apply the fusion operator on the set of all sources and provide the resulting information. In this work, we studied and proposed a method to combine information using Formal Concept Analysis in particular Pattern Structures. This method allows us to associate any subset of sources with its information fusion result. Then once a fusion operator is chosen, a concept lattice is built. The concept lattice gives an interesting classification of fusion results and it keeps a track of the information origin. When the fusion global result is too imprecise, the method enables the users to identify what maximal subset of sources would support a more precise and useful result. Instead of providing a unique fusion result, the method yields a structured view of partial results labeled by subsets of sources. In this thesis, we studied the numerical information represented in the framework of possibility theory and we used three fusion operators to built the concept lattice. We applied this method in the context of agronomy when experts have to estimate several characteristics values coming from several sources for computing an environmental risk