Peter Butka

On equivalence of conceptual scaling and generalized one-sided concept lattices

The methods of conceptual scaling and generalized one-sided concept lattices represent different possibilities on how to deal with many-valued contexts. We briefly describe these methods and prove that they are equivalent. In particular, we show that the application of these two approaches to a given many-valued context yields the same closure system on the set of all objects. Based on this equivalence, we propose a possible attribute reduction of one-sided formal contexts.

Design and implementation of incremental algorithm for creation of generalized one-sided concept lattices

In this paper we describe incremental algorithm for generalized one-sided concept lattices based on the Galois connections within Formal Concept Analysis (FCA) framework, which allows to analyse object-attribute models with different structures for truth values of attributes. Therefore, this method provide interesting opportunity for researcher or data analyzer to work with any type of attributes without the need for specific unified preprocessing. The result is that such algorithm can be very useful for any object-attribute models with non-homogenous attributes types, what is quite typical in data mining or online analytical tools. Moreover, it allows to create same FCA-based output in form of concept lattice as in any other case with very precise definition of attribute values and their interpretation. Description of algorithm is extended with practical details regarding its implementation and illustrative example based on the real data from analysis of the secondary school learning process.

Reduction of Concepts from Generalized One-Sided Concept Lattice Based on Subsets Quality Measure

One of the conceptual methods in data mining area is based on the onesided concept lattices, which belongs to approaches known as Formal ConceptAnalysis (FCA). It provides an analysis of objects clusters according to the set of fuzzy attributes. The specific problem of such approaches is sometimes large number of concepts created by the method, which can be crucial for the interpretation of the results and their usage in practice. In this chapter we describe the method for evaluation of concepts from generalized one-sided concept lattice based on the quality measure of objects subsets. Consequently, this method is able to select most relevant concepts according to their quality, which can lead to useful reduction of information from concept lattice. The usage of this approach is described by the illustrative example.

Representation of Fuzzy Concept Lattices in the Framework of Classical FCA

We describe a representation of the fuzzy concept lattices, defined via antitone Galois connections, within the framework of classical Formal Concept Analysis. As it is shown, all needed information is explicitly contained in a given formal fuzzy context and the proposed representation can be obtained without a creation of the corresponding fuzzy concept lattice.

A Proposal of the Information Retrieval System Based on the Generalized One-Sided Concept Lattices

One of the important issues in information retrieval is to provide methods suitable for searching in large textual datasets. Some improvement of the retrieval process can be achieved by usage of conceptual models created automatically for analysed documents. One of the possibilities for creation of such models is to use well-established theory and methods from the area of Formal Concept Analysis. In this work we propose conceptual models based on the generalized one-sided concept lattices, which are locally created for subsets of documents represented by object-attribute table (document-term table in case of vector representation of text documents). Consequently, these local concept lattices are combined to one merged model using agglomerative clustering algorithm based on the descriptive (keyword-based) representation of particular lattices. Finally, we define basic details and methods of IR system that combines standard full-text search and conceptual search based on the extracted conceptual model.

Semantically-enhanced extension of the discussion analysis algorithm in SAKE

In this article we describe an approach for semantic-based analysis of discussions within semantic-based groupware system (GWS) in SAKE project. SAKE (semantic agile knowledge-based e-government) is a STREP Project sponsored by the European Union starting March in 2006. The overall objective of SAKE is to specify, develop and deploy a holistic framework and supporting tools for an agile knowledge-based e-government that will be sufficiently flexible to adapt to changing and diverse environments and needs. We give a brief overview of the approach that will be applied for evaluation of discussion, discussions threads and discussion posts. Part of the approach is also an analysis of the discussants regarding positive or negative reactions on their contributions, extended by usage of concepts from argumentation ontology. Main goal is to identify some rating of the users involved in the discussion and support moderators in evaluation of discussion result and/or identify discussants skills useful for another similar case discussion.

Multiple Data Tables Processing via One-Sided Concept Lattices

One-sided concept lattices introduce data mining method from the area of Formal Concept Analysis (FCA) for analysis of objects clusters according to the set of fuzzy attributes. Currently, most of the methods for creation of one-sided concept lattices process only data tables with one type of truth value structure. In this chapter we describe closure operator, which corresponds to the intersection of particular closure systems obtained from various object-attribute models with different types of attributes. Each particular closure system is defined via one-sided concept lattices approaches applicated for particular data tables.

Open Collaboration in Policy Development: Concept and Architecture to Integrate Scenario Development and Formal Policy Modelling

Along the demands for good governance and open government, policymakers need concise, reliable and up-to-date information to respond to society’s problems and affairs in an efficient and effective way. Likewise, stakeholders affected by a particular policy call for transparency, accountability and trustworthiness in political decision-making. Along the evolution of information society that leads to increasing digitisation of information and knowledge artefacts and public services, citizens more and more request direct involvement in policymaking. In this chapter, we introduce a comprehensive and innovative approach to collaborative policy development. The approach integrates collaborative scenario building and formal policy modelling via an integrated ICT toolbox. Stakeholders are collaboratively involved in the scenario development as well as in the evaluation of simulation outcomes. To bridge the gap between narrative texts of stakeholder-generated scenarios (evidenced through background documents of the policy to be discussed) and formal policy models (generating model-based scenarios), the approach introduces conceptual modelling, which enables the different stakeholders to better understand the policy context and to support semi-automatic transformation of text statements into formal statements and agent descriptions. A consequence of the agent-based modelling approach used is that the justifications for expectations of the stakeholders are made precise, explicit and linked to evidence, and this process provides for the monitoring of ongoing policy implementation.

On generation of one-sided concept lattices from restricted context

In this paper the relationship between one-sided concept lattices and their restricted version is described. One-sided concept lattices are based on the Galois connections within Formal Concept Analysis (FCA) framework, which allows to analyse object-attribute models with different structures for truth values of attributes. We present the approach for generation of one-sided concept lattices from restricted formal context, which is obtained from given one by omitting some subset of the set of all attributes. The resulted algorithm for such restricted problem is described, together with the discussion on its correctness.

On some complexity aspects of generalized one-sided concept lattices algorithm

In this paper we provide some complexity aspects of incremental algorithm for creation of generalized one-sided concept lattices. The novelty of this algorithm is in its possibility to work with different types of attributes and produce one-sided concept lattice from the generalized one-sided formal context. As it is shown in the paper, the complexity of the algorithm is in general exponential. However, in practice it is reasonable to consider special cases, where the number of attributes is fixed. Then complexity of presented algorithm asymptotically becomes linear function depending on the number of objects in formal context.