Jozef Pócs

Note on generating fuzzy concept lattices via Galois connections

The aim of this paper is to compare an approach of creating fuzzy concept lattices proposed by Popescu with several other approaches. Particularly, we show that this approach is in some way equivalent to the approach of Krajci called generalized concept lattices. We also give a straightforward generalization of Popescus approach to non-homogeneous cases.

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.

On possible generalization of fuzzy concept lattices using dually isomorphic retracts

We provide a generalization of fuzzy concept lattices based on so-called weak Galois connections. Generalization is that instead of dually isomorphic closure systems we consider dually isomorphic retracts of complete lattices. We also give a generalization of the concept lattices with hedges, proposed by Belohlavek and Vychodil, based on composition of interior operators with Galois connections.

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.

A new characterization of the discrete Sugeno integral

We have completely characterized compatible aggregation functions on 0,1.The compatibility is a new characteristic property of Sugeno integrals.We have shown that the scale invariant normed utility functions are just Sugeno integrals. We introduce a new property of the discrete Sugeno integrals which can be seen as their characterization, too. This property, compatibility with respect to congruences on 0, 1, stresses the importance of the Sugeno integrals in multicriteria decision support as well.

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.

Generalized one-sided concept lattices with attribute preferences

The main aim of this paper is to introduce the preference relations on generalized one-sided concept lattices, which represent a fuzzy generalization of FCA with classical object clusters and fuzzy attributes. In our case a preference relation is modeled by a linear well quasi-order on the set of all attributes. We describe concept forming operators based on a Galois connection, which is defined between the power set of objects and the fuzzy sets of attributes with lexicographic order induced by the preference relation. The representation theorem for such kind of concept lattices is also presented.

On concept reduction based on some graph properties

The theory of concept lattices represents a well established and widely used conceptual data-mining method. Considering additional information represented by a graph structure on a set of objects, we propose a reduction of concepts. Using graph-theoretical point of view on FCA together with simple probabilistic arguments we derive the mean value of the cardinality of the reduced hierarchical structure.

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.