Formal Concept Analysis

Several fuzzifications of formal concept analysis have been proposed to deal with uncertain information. In this paper, we focus on concept lattices under a multiadjoint paradigm, which enriches the language providing greater flexibility to the user in that she can choose from a number of different connectives. Multi-adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature, the main results of the paper being the representation theorem of this paradigm and the embedding of other well-known approaches.

Analysis may be combined to obtain a formalization of Elementary Logic which is useful for knowledge representation and processing. For this, a translation of conceptual graphs to formal contexts and concept lattices is described through an example. Using a suitable mathematization of conceptual graphs, basics of a uni ed mathematical theory for Elementary Logic are proposed.

This paper presents an information retrieval methodology which uses Formal Concept Analysis in conjunction with semantics to provide contextual answers to users' queries. User formulates a query on a set of heterogeneous data sources. This set is semantically unified by the proposed notion conceptual context. A context can be global: it defines a semantic space the user can query -or instantaneous-it defines the current position of the user in the semantic space. Our methodology consists first in a pre-treatment providing the global conceptual context and then in an online contextual processing of users' requests, associated to an instantaneous context. This methodology can be applied to heterogeneous data sources such as web pages, databases, email, personal documents and images, etc. One interest of our approach is to perform a more relevant and refined information retrieval and contextual navigation, closer to the users' expectation.

Grooming is the process by which pedophiles try to find children on the internet for sex-related purposes. In chat conversations they may try to establish a connection and escalate the conversation towards a physical meeting. Till date no effective methods exist for quickly analyzing the contents, evolution over time, the present state and threat level of these chat conversations. In this paper we propose a novel method based on Temporal Relational Semantic Systems, the main structure in the temporal and relational version of Formal Concept Analysis. For rapidly gaining insight into the topics of chat conversations we combine a linguistic ontology for chat terms with conceptual scaling and represent the dynamics of chats by life tracks in nested line diagrams. To showcase the possibilities of our approach we used chat conversations of a private American organization which actively searches for pedophiles on the internet.

Safety critical software requires integrating verification techniques in software development methods. Software architectures must guarantee that developed systems will meet safety requirements and safety analyses are frequently used in the assessment. Safety engineers and software architects must reach a common understanding on an optimal architecture from both perspectives. Currently both groups of engineers apply different modelling techniques and languages: safety analysis models and software modelling languages. The solutions proposed seek to integrate both domains coupling the languages of each domain. It constitutes a sound example of the use of language engineering to improve efficiency in a software-related domain. A model-driven development approach and the use of a platform-independent language are used to bridge the gap between safety analyses (failure mode effects and criticality analysis and fault tree analysis) and software development languages (e.g. unified modelling language). Language abstract syntaxes (metamodels), profiles, language mappings (model transformations) and language refinements, support the direct application of safety analysis to software architectures for the verification of safety requirements. Model consistency and the possibility of automation are found among the benefits.

We introduce the notion of iceberg concept lattices and show their use in knowledge discovery in databases. Iceberg lattices are a conceptual clustering method, which is well suited for analyzing very large databases. They also serve as a condensed representation of frequent itemsets, as starting point for computing bases of association rules, and as a visualization method for association rules. Iceberg concept lattices are based on the theory of Formal Concept Analysis, a mathematical theory with applications in data analysis, information retrieval, and knowledge discovery. We present a new algorithm called TITANIC for computing (iceberg) concept lattices. It is based on data mining techniques with a level-wise approach. In fact, TITANIC can be used for a more general problem: Computing arbitrary closure systems when the closure operator comes along with a so-called weight function. The use of weight functions for computing closure systems has not been discussed in the literature up to now. Applications providing such a weight function include association rule mining, functional dependencies in databases, conceptual clustering, and ontology engineering. The algorithm is experimentally evaluated and compared with Ganter's Next-Closure algorithm. The evaluation shows an important gain in efficiency, especially for weakly correlated data. Ó

Las diferencias existentes entre generaciones van más allá que las derivadas de la propia edad y los estereotipos; los cambios tecnológicos o las jerarquías, como la de alumno-profesor, crean una brecha que se produce con el cambio social, cuando los jóvenes adquieren una visión diferente del mundo de la que tienen sus mayores que se mantiene durante toda su vida, generando así distancias en el entendimiento entre los grupos coetáneos, también conocidas como brechas. En la presente investigación se pretende realizar una visualización de las  brechas, a través de la aplicación de la teoría del Formal Concept Analysis, para determinar la cercanía y entendimiento entre los actores de dos grupos generacionales (profesores y alumnos) a partir de sus actividades en el contexto educativo de una Universidad pública seleccionada, partiendo de las brechas generacional, cognitiva y digital.

FPM (Frequent Pattern Mining) is a data mining paradigm to extract informative patterns from massive datasets. Researchers have developed numerous novel algorithms to extract these patterns. Unfortunately, the focus primarily has been on a small set of popular patterns (itemsets, sequences, trees and graphs) and no framework for integrating the FPM process has been attempted. In this paper we introduce DMTL, a generic pattern mining library which fuses theoretical concepts from formal concept analysis and generic ...

The objective of this research is to extract triadic association rules from a triadic formal context K := (K1, K2, K3, Y) where K1, K2 and K3 respectively represent the sets of objects, properties (or attributes) and conditions while Y is a ternary relation between these sets. Our approach consists to define a procedure to map a set of dyadic association rules into a set of triadic ones. The advantage of the triadic rules compared to the dyadic ones is that they are less numerous and more compact than the second ones and convey a richer semantics of data. Our approach is illustrated through an example of ternary relation representing a set of Customers who purchase theirProducts from Suppliers. The algorithms and approach proposed have been validated with experimentations on large real datasets.

With the emergence of Web 2.0, user-generated metadata or so-called folksonomies facilitates management of digital content in the World Wide Web. The folksonomies have increasingly become a viable alternative for knowledge seekers to classify their knowledge (resources) and navigate the resources. Traditionally, in expert systems, taxonomy has been fulfilling these roles. However, in a taxonomy, the taxonomic structures are defined by the taxonomists or professional experts of the domain which often do not reflect user vocabulary. In addition, the terms of the taxonomy become outdated very fast which in turn compromises the efficiency and effectiveness of knowledge classification and navigation. On the other hand, maintenance of the taxonomy is time consuming and exhausted. This paper presents taxonomy and folksonomy integration algorithm, namely TaxoFolk to integrate the folksonomy into a taxonomy to enhance knowledge classification and navigation. The output is a hybrid taxonomyfolksonomy structure. The TaxoFolk algorithm comprises of data mining techniques, namely Formal Concept Analysis (FCA), ID3 classification and Simple Matching Coefficients (SMC). Three different taxonomy domains and its folksonomy are used to setup the experiments to identify and to evaluate the threshold values for filtering infrequent tags and invalid tags to automate the TaxoFolk algorithm to integrate a filtered folksonomy with a pre-defined taxonomy for enhancing knowledge navigation. The conducted experiments have ascertained the most appropriate thresholds values for effective building of TaxoFolk structure.

This thesis presents an analysis of the nature of volunteered geographical information (VGI) and on its applicability for use in a spatial data infrastructure (SDI) to supplement official and commercial sources, particularly given the ease with which ordinary people can document their environment, experiences, perspectives and prejudices, share them widely and rapidly, and even query anyone else’s content. For this research, taxonomies and repositories of such information were examined qualitatively and using formal concept analysis (FCA). Further, this thesis attempts to reflect on the context for SDIs and VGI and the challenges and opportunities for both.

An SDI is an evolving concept for facilitating and coordinating the management and sharing of geospatial data, with services, metadata, products, standards and inter-organisation arrangements and structures. It can take long to establish an SDI; some have failed and they have competition. In South Africa, the National Development Plan has an objective to establish a national spatial observatory: it is part of an SDI with its own value-add data, and products provided through the SDI or directly to its participants. The Spatial Data Infrastructure Act established the South African Spatial Data Infrastructure and its Committee for Spatial Information.

Creating vast quantities of user-generated content (UGC) has been enabled by the pervasiveness, power and affordability of inter-networking, social media, virtual communities, applications and mobile devices. VGI is user-generated content with geospatial components, or user-generated geospatial content.

VGI can contribute successfully to an SDI, at the local, national, regional or global level. VGI can extend the reach in time and space of official mapping agencies and others contributing to an SDI, because of the sheer volume of humans and their devices acting together or independently, as sensors, recorders and disseminators. VGI; repositories of VGI; innovative integration of content, applications and services (mashups); crowd sourcing and new geographical theories (psychogeography, social theory, social justice, ethics, etc) all challenge the traditional business models of SDIs.

However, metadata, quality, classification and standards can be challenges for VGI. Further, while some VGI can be useful, other VGI can be spurious, misleading or wrong. There are also different interpretations over what is actually VGI.

To provide context for the exposition, this thesis also examines terminology, geospatial data, classification, folksonomies, virtual globes, inter-networking, the limitations of the Internet, controlling the Internet, privacy, exploiting content, social media, curation, the digital divide, citizen science, crowd sourcing, neogeography, metadata, quality, standards and formal concept analysis (FCA). To determine the nature of VGI and its suitability for an SDI, this thesis investigates various taxonomies of UGC, VGI and citizen science; assesses qualitatively their discrimination adequacy using VGI repositories; and assesses them using FCA.

This thesis also presents original research contributions, to information science, geographical information science and theoretical computer science. For FCA it presents lemmas on stability in a lattice (providing lower and upper bounds for intensional and extensional stability indices), it shows there is value in instability in a lattice when assessing a taxonomy (representing extreme values rather than noise) and it presents stability exploration, a possible decision support tool. It describes the four stages for recognising the quality of a resource, it reports on a survey of geographical information professionals on VGI, SDIs and virtual globes, and it clarifies the differences between UGC, VGI, citizen science, crowd sourcing and neogeography, which can be confused with one another. Finally, this thesis explains why the Internet cannot be controlled.

Thesis (PhD)--University of Pretoria, 2016. © 2016 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.

Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of concept and concept hierarchy. Only after more than a decade of development, the connections to the philosophical logic of human thought became clearer and even later the connections to Piaget’s cognitive structuralism which Thomas Bernhard Seiler convincingly elaborated to a comprehensive theory of concepts in his recent book [Se01]. It is the main concern of this paper to show the surprisingly rich correspondences between Seiler’s multifarious aspects of concepts in the human mind and the structural properties and relationships of formal concepts in Formal Concept Analysis. These correspondences make understandable, what has been experienced in a great multitude of applications, that Formal Concept Analysis may function in the sense of transdisciplinary mathematics, i.e., it allows mathematical thought to aggregate with other ways of thinking and thereby to support human thought and action.

Currently, the bulk of applications of Formal Concept Analysis (FCA) in software engineering have focussed on software maintenance and re-engineering. In this thesis we broaden the approach by applying FCA to a number of early-phase activities within the software engineering life-cycle.

This thesis proposes a methodology, notation/theory, and software framework for organising documents using formal concept analysis. The documents are organised for the purposes of retrieval and analysis using background information in the form of a taxonomy of terms. An emphasis is placed on the development of a methodology that employs scalable computer pro- grams to assist humans in the process of organisation, retrieval and analysis of document collections.
The text retrieval community has also been concerned with the organisation of documents. The work outlined in this thesis makes use of the results of the text retrieval community at its lowest layer. Above this layer formal concept analysis is used as a mechanism to allow users to organise document collections using views determined by small numbers of attributes. These views, also known as scales, can make a mixture of coarse and specific distinctions between documents, and are either selected or created by the users to make precisely the distinctions between documents that are important to their current tasks.
The primary tool for the presentation of the results of formal concept analysis is a line diagram. The effectiveness of the presentation of information contained in a line diagram is heavily dependent on the quality of the diagram. To support users in arriving at a quality diagram for a newly created view, graph drawing algorithms are adapted to the special case of determining a good layout for a concept lattice. This task is different from traditional graph layout problems because lattices exhibit a high degree of structure which should be exploited and made evident in the final diagram. A new layout algorithm is proposed that combines a layered diagram approach and an additive diagram methodology. This new hybrid algorithm is shown to produce better diagrams than other adapted graph drawing algorithms.

FAIA covers all aspects of theoretical and applied artificial intelligence research in the form of monographs, doctoral dissertations, textbooks, handbooks and proceedings volumes. The FAIA series contains several sub-series, including "Information Modelling and Knowledge Bases" and "Knowledge-Based Intelligent Engineering Systems". It also includes the biennial ECAI, the European Conference on Artificial Intelligence, proceedings volumes, and other ECCAI-the European Coordinating Committee on Artificial Intelligence-sponsored publications. An editorial panel of internationally well-known scholars is appointed to provide a high quality selection.

The transfer of tacit knowledge is important in ensuring that an organisations most valuable assets do not walk out the door. While much controversy surrounds the definition of tacit knowledge and whether it can be captured, in this paper we follow a psychological approach based on the work of Sternberg at Yale that seeks to measure tacit knowledge via the capture of responses to workplace scenarios. Focusing on the information technology (IT) workplace , we have developed a tacit knowledge inventory which forms part of a questionnaire given to experts and non-experts in three separate IT organisations. In psychology, descriptive statistics are typically used to analyse the responses. We have chosen a more qualitative and visual approach and have used formal concept analysis (FCA) for data analysis that better suits our small sample size. Using FCA we were able to identify participants that responded similarly to the peer-identified experts. In this way the organisation is alerted to the important role these individuals potentially play.

We can fill the gap between theory (of ambitious teacher educa- tion) and practice (in mathematics classrooms) more easily, when we take into account that teacher education is not only explicit acquisition of knowl- edge and methods but also development of individual personal constructs of mathematics and mathematics education. But how can we get knowledge about the development of individual

Abstract - Digital medical image plays an important role in the field of Telemedicine, but patient privacy and other security issues are still coming under threats from unauthorized users. Watermarking has become essential and required for proving the identity of the owner, as well as authorizing use of images and also protecting copyrighted material from illegal access. Authorizing use and copyright protection as parameters of an image, especially of a medical image, are strongly related to robustness and complexity, imperceptibility and capacity as parameters of watermarking. Medical images have a special structure which comprises header and body blocks. The region of non interest (NROI) in the body of a medical image is the most suitable area for embedding watermark to prevent the degradation of the medical image. In our paper, we propose a novel watermarking approach in the spatial domain, based on formal concept analysis (FCA). FCA finds the optimal position for watermark embedding in NROI of the medical image. Our watermark is built from some existing information in the DICOM header (IODs). Experimental results indicate that the proposed approach would offer us high robustness with less complexity, imperceptible embedding and low payload compared with the existing watermarking approaches.

Keywords - FCA; Watermarking; Spatial Domain; Attacks; Robustness.

In this paper the problems of deriving a taxonomy from a text and concept-oriented text segmentation are approached. Formal Concept Analysis (FCA) method is applied to solve both of these linguistic problems. The proposed segmentation method offers a conceptual view for text segmentation, using a context-driven clus-tering of sentences. The Concept-oriented Clustering Segmentation algorithm (COCS) is based on k-means linear clustering of the sentences. Experimental results obtained using COCS algorithm are presented. 1.

Supervised classification is a spot/task of data mining which consists in building a classifier from a set of examples labeled by their class (learning step) and then predicting the class of new examples with a classifier (classification step). In supervised classification, several approaches were proposed such as: Induction of Decision Trees, and Formal Concept Analysis. The learning of formal concepts is based, generally, on the mathematical structure of Galois lattice (or concept lattice). The complexity of generation of Galois lattice, limits the application fields of these systems. In this paper, we present several methods of supervised classification based on Formal Concept Analysis. We present methods based on concept lattice or sub lattice. We also present the boosting of classifiers, an emerging technique of classification. Finally, we propose the boosting of formal concepts: a new adaptive approach to build only a part of the lattice including the best concepts. These concepts are used as classification rules. Experimental results are given to prove the interest of the proposed method.

This book contains thirteen chapters. There are (1) Preliminary, (2) Formal Context Based on Pictorial Diagram, (3) Partially-Ordered Attribute Diagram, (4) Non-matrix Knowledge Reduction Method for Fuzzy Context, (5) Interval-Set-Based Concept Lattice, (6) Axiality Concept Lattice and Its Attribute Redction, (7) Representation of Special Ordered Structure Based on FCA, (8) Decision Logic of Concept Lattice, (9) Attribute Reduction in Intuitionistic Fuzzy Generalized Consistent Decision Context, (10) Two-way Learning Based on FCA in Fuzzy Datasets, (11) Rule comparison Between Conept Lattice and Multi-granulation Rough Set, (12) Attribute Topology and Its Application, and (13) Triadic Concept Analysis.

Medical diagnosis process vary in the degree to which they attempt to deal with different complicating aspects of diagnosis such as relative importance of symptoms, varied symptom pattern and the relation between diseases them
selves. Based on decision theory, in the past many mathematical models such as crisp set, probability distribution, fuzzy set, intuitionistic fuzzy set were developed to deal with complicating aspects of diagnosis. But, many such models are failed to include important aspects of the expert decisions. Therefore, an effort has been made to process inconsistencies in data being considered by Pawlak with the introduction of rough set theory. Though rough set has major advantages over the other methods, but it generates too many rules that create many difficulties while taking decisions. Therefore, it is essential to minimize the decision rules. In this paper, we use two processes such as preprocess and post process to mine suitable rules and to explore the relationship among the attributes. In pre process
we use rough set theory to mine suitable rules, whereas in post process we use formal concept analysis from these
suitable rules to explore better knowledge and most important factors affecting the decision making.

The density and viscosity of solutions of methanol, ethanol, glucose and sucrose in distilled water at various temperatures were reported and compared with the available literature data. Data obtained was used to understand the interactions of substrates in solution. Influence of concentration of substrates and salts on strengthening or weakening of these interactions was evaluated. Apparent molar volumes were estimated from
density data of different systems. The presence of various polar groups in the molecules showed varying interactions and there by the viscosity also varies. The results reveal that the molecular interactions strongly depend on the polarity and the substituents attached to the hydroxyl groups. Influence of nature of substrates and the other ions commonly present in water is discussed. Also, we have analyzed the relations between alcohols and their properties using a data analysis technique, Formal Concept Analysis (FCA).

The thesis of Mehdi Kaytoue addressed the important problem of mining patterns in numerical data, also known as quantitative itemset problem. Usually, numerical data are turned into binary data from which well known itemsets and association rules are extracted. Extracting those patterns is a first step for knowledge discovery processes. Nevertheless, transforming the data faces a trade-off: it comes either with loss of information, or hard computational properties of the resulting binary data. The proposed approach is defined within a well known and mathematically defined framework: formal concept analysis. It allows the mining of numerical patterns (without binarization) in several fields such as lattice-based classification, knowledge discovery in databases and information fusion.

A MATHEMATICAL MODEL is presented to define new inclusions, intersections and unions as alternatives to the usual ones between crisp and fuzzy subsets. In particular, the concept of “the non-trivial content of the empty set ∅” is analyzed.
This proposed model is based on the interconnection of two consolidated mathematical concepts in specialized literature:
One of them, (which belongs to the field of image processing using Mathematical Morphology techniques), is that of activity  ordering and that we use here in the general context of lattices (L, ≤) and in particular in that of Boolean Algebras.
The other consists of a version in distributive lattices (L, ≤) of the symmetric difference operator Δ, a classic concept in Set Theory.
The utility of the model is illustrated in the following fields: analysis of risk maps, (areas of avalanches, risk of fires, landslides, earthquakes, ...), as well as maps with contour lines: (isochrons, isotherms, salinity , rainfall, intensity of earthquakes, ...). Also in data pre-processing for “Data Mining” tasks and in “Data Analysis with Uncertainty”.
A special section is dedicated to the application of the model in Digital Image Processing using Mathematical Morphology techniques.
Finally, it is justified that the model can be useful in other fields such as Analysis of Formal Concepts, Probability and in theoretical contexts such as Topology.

FPM (Frequent Pattern Mining) is a data mining paradigm to extract informative patterns from massive datasets. Researchers have developed numerous novel algorithms to extract these patterns. Unfortunately, the focus primarily has been on a small set of popular patterns (itemsets, sequences, trees and graphs) and no framework for integrating the FPM process has been attempted. In this paper we introduce DMTL, a generic pattern mining library which fuses theoretical concepts from formal concept analysis and generic ...

Among many other knowledge representations formalisms, Ontologies and Formal Concept Analysis (FCA) aim at modeling 'concepts'. We discuss how these two formalisms may complement another from an application point of view. In particular, we will see how FCA can be used to support Ontology Engineering, and how ontologies can be exploited in FCA applications. The interplay of FCA and ontologies is studied along the life cycle of an ontology: () FCA can support the building of the ontology as a learning technique. (¡) The established ontology can be analyzed and navigated by using techniques of FCA.

In the present study the use of Knowledge Space Theory (KST), jointly with Formal Concept Analysis (FCA), is proposed to develop a formal representation of the relations between the items of a questionnaire and a set of psychodiagnostic criteria. This formal representation can be used to develop an efficient adaptive tool for psychological assessment. show some interesting connections between KST and FCA; these connections are applied to construct knowledge structures starting from a formal context representing the relations between items and criteria. The proposed general methodology has been applied, as an example, to the Maudsley Obsessive-Compulsive Questionnaire. We used a data-set provided by a sample of patients with a diagnosis of Obsessive-Compulsive Disorder to validate the obtained structures. The parameters of the Basic Local Independence Model (BLIM) have been estimated for the obtained knowledge structures. The fit of each model has been tested by parametric bootstrap because of the sparseness of the derived data matrix. Results are discussed in light of both psychological and methodological relapses. In particular we propose a re-interpretation of the BLIM parameters that seems suitable for testing reliability and construct validity; furthermore it is pointed out how the obtained structures could represent the starting point for the development of a computerized assessment tool. B128 4

Formal concept analysis and Galois lattices in general are increasingly used for large contexts that are automatically generated. As the size of the resulting datasets may grow considerably, it becomes essential to keep the algorithmic complexity of the analysis procedures as low as possible. This paper presents an e cient algorithm that computes the Hasse diagram of a Galois lattice from the lattice ground set, i.e., the set of all concepts. The algorithm performs an element-wise completion of the lattice according to a linear extension of the lattice order. This requires only a limited number of comparisons between concepts and therefore makes the global algorithm very e cient. In fact, its asymptotic time complexity i s almost linear in the number of concepts. Consequently, the joint use of our algorithm with an e cient procedure for concept generation yields a complete procedure for building the Galois lattice.

Pān . ini defines the sound classes involved in grammatical rules by pratyāhāras, i.e., a two-letter code based on the order of the sounds in theŚivasūtras. In the present paper we demonstrate that Pān . ini's pratyāhāra method is generalizable to the description of the phonological systems of other languages by applying it to the sound classes and phonological alternations of German. Furthermore, we compare Pān . ini's pratyāhāra technique with the technique of describing phonological classes by phonological features, which is more common in Western phonology. It turns out that pratyāhāras perform better than features for the description of our sample of German phonological processes if one considers the quality criterion for class-description devices proposed by which is based on the ratio of describable to actual classes.

JOHN CORCORAN,Tarski on logical notions. Journal of Symbolic Logic. 53 (1988) 1291.

This is a critical and analytical discussion of Alfred Tarski's 1973 Buffalo lecture. As Tarski requested, I edited and introduced it for HPL. The 1986 HPL paper has been at the top of HPL's "most-cited" list.



1986. Alfred Tarski's "What are Logical Notions?" (Edited and introduced), History and Philosophy of Logic 7, 143–154.  MR88b:03010
https://www.academia.edu/12410865/Alfred_Tarskis_What_are_Logical_Notions_Edited_and_introduced_by_John_Corcoran_

Concept-cognitive learning, as an interdisciplinary study of concept lattice and cognitive learning, has become a hot research direction among the communities of rough set, formal concept analysis and granular computing in recent years. The main objective of concept-cognitive learning is to learn concepts from a give clue with the help of cognitive learning methods. Note that this kind of studies can provide concept lattice insight to cognitive learning. In order to deal with more complex data and improve learning efficiency, this paper investigates parallel computing techniques for concept-cognitive learning in terms of large data and multi-source data based on granular computing and information fusion. Specifically, for large data, a parallel computing framework is designed to extract global granular concepts by combining local granular concepts. For multi-source data, an effective information fusion strategy is adopted to obtain final concepts by integrating the concepts from all single-source data. Finally, we conduct some numerical experiments to evaluate the effectiveness of the proposed parallel computing algorithms.

We present a novel approach to the automatic acquisition of taxonomies or concept hierarchies from a text corpus. The approach is based on Formal Concept Analysis (FCA), a method mainly used for the analysis of data, i.e. for investigating and processing explicitly given information. We follow Harris' distributional hypothesis and model the context of a certain term as a vector representing syntactic dependencies which are automatically acquired from the text corpus with a linguistic parser. On the basis of this context information, FCA produces a lattice that we convert into a special kind of partial order constituting a concept hierarchy. The approach is evaluated by comparing the resulting concept hierarchies with hand-crafted taxonomies for two domains: tourism and finance. We also directly compare our approach with hierarchical agglomerative clustering as well as with Bi-Section-KMeans as an instance of a divisive clustering algorithm. Furthermore, we investigate the impact of using different measures weighting the contribution of each attribute as well as of applying a particular smoothing technique to cope with data sparseness.

Content analysis as a method in social sciences is used to systematically explore textual data. Data resulting from content analysis can be made transparent by saving it in a conceptual data system. This supports its interpretation and reexamination and the process of interpretative theory building. By means of an example of a conceptual data system from musicology, the possibilities and restrictions of this new approach in computer-aided qualitative text research are analyzed. Finally, the approach is discussed as a general method of qualitative formal theory building in the context of content analysis.

Motives are short melodic, rhythmic, and/or harmonic patterns repeated either exactly or in varied forms and have long been recognized as important elements of musical structure. Less well explored is the relationship between motives and their manifestation in performance, and the perception thereof. Expressive motives originating in performance - which we term "performance motives" - are also of considerable interest

In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal concept theory where we have constructed the L-Fuzzy concept lattice.

Introduced by Rudolf Wille in the mid-80s, Formal Concept Analysis (FCA) is a mathematical framework that offers conceptual data analysis and knowledge discovery. FCA analyzes the data, which is represented in the form of a formal context, that describe the relationship between a particular set of objects and a particular set of attributes. From the formal context, FCA produces hierarchically ordered clusters called formal concepts and the basis of attribute dependencies, called attribute implications. All the concepts of a formal context form a hierarchical complete lattice structure called concept lattice that reflects the relationship of generalization and specialization among concepts. Several algorithms are proposed in the literature to extract the formal concepts from a given context. The objective of this chapter is to analyze, demonstrate, and compare a few standard algorithms that extract the formal concepts. For each algorithm, the analysis considers the functionality, output, complexity, delay time, exploration type, and data structures involved.