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18th International Multidisciplinary Scientific Geoconference, SGEM 2018

作者： Ivanová, Monika Michaeli, Eva Solár, Vladimír Škrabuľáková, Erika Fecková Department of Geography and Applied Geoinformatics Faculty of Humanities and Natural Sciences University of Prešov Slovakia Institute of Control and Informatization of Production Processes Faculty of Mining Ecology Process Control and Geotechnology Technical University of Košice Slovakia

ISBN: (纸本)9786197408355

The main aim of the contribution is development the spatial structure analysis of the landscape on the basis of evaluation the classes of land cover and their extension in the model territory in two time horizons (1956, 2009) on the bases of GIS technologies with using superstructure software Patch Analyst for ArcView GIS and as well as using mathematical and statistical methods which is each other combined also with traditional geographic field research. These methods were complemented by the results of explorative analysis presented via Chernoff’s faces that showed some similarities and differences in the structure of patches in both time horizons. The input matrix of values for the usage of multidimensional statistical hierarchical and non-hierarchical clustering methods was built up of the selected landscape-metrics indices quantifying the specific properties of the spatial structure of patches in the classes of land cover. The model territory is located in Eastern Slovakia on the border of two genetically different tectonical units the Vihorlatské vrchy mts. in the north and the Východoslovenská nížina lowland in the south. © SGEM2018.

关键词： Geographic information systems

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Niels henrik abel and the birth of fractional calculus

arXiv

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arXiv 2018年

作者： Podlubny, Igor Magin, Richard L. Trymorush, Iryna Institute of Control and Informatization of Production Processes BERG Faculty Technical University of Kosice B. Nemcovej 3 Kosice04200 Slovakia Department of Bioengineering University of Illinois 851 S Morgan St ChicagoIL60607 United States

Dedicated to Professor Virginia Kiryakova on the occasion of her 65th birthday and the 20th anniversary of FCAA In his first paper on the generalization of the tautochrone problem, that was published in 1823, Niels Henrik Abel presented a complete framework for fractional-order calculus, and used the clear and appropriate notation for fractional-order integration and *** Codes 01A55, 01A75 Copyright © 2018, The Authors. All rights reserved.

关键词： Calculations

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Usage of clustering methods in mathematics, geoinformatics and related fields of university study 17

Usage of clustering methods in mathematics, geoinformatics a...

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17th IEEE International Carpathian control Conference, ICCC 2016

作者： Škrabuláková, Erika Fecková Ivanová, Monika Michaeli, Eva Institute of Control and Informatization of Production Processes Faculty of Mining Ecology Process Control and Geotechnology Technical University of Košice Slovakia Department of Geography and Applied Geoinformatics Faculty of Humanities and Natural Sciences University of Prešov in Prešov Slovakia

ISBN: (纸本)9781467386067

In the paper we compare the hierarchical clustering methods with the non-hierarchical ones at an example of analysis of similarity's rate of European Union universities. The main aim of the collation is to find out whether the clusters obtained by different methods correspond in some sense. There are 3 largest universities per each state of the European Union in our database The main criterion of choice was the number of students studying at each university. A portion of our database contains data about the possibilities of study mathematics, geodesy, GIS and geoinformatics at the chosen EU universities. As the quality of the education partially depends on the ratio of students per pedagogue we tried to exaluate this parameter as well. © 2016 IEEE.

关键词： Cluster analysis

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Basic theorem as representation of heterogeneous concept lattices

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Frontiers of Computer Science 2015年第4期9卷 636-642页

作者： Jozef POCS Jana POCSOVA Palacky University Olomouc Department of Algebra and Geometry Olomouc 779 00 Czech Republic Mathematical Institute Slovak Academy of Sciences Kosice 040 01 Slovakia Technical University of Kosice BERG Faculty Institute of Control and Informatization of Production Processes Ko~ice 043 84 Slovakia

We propose a method for representing heteroge- neous concept lattices as classical concept lattices. Particu- larly, we describe a transformation of heterogeneous formal context into a binary one, such that corresponding concept lattices will be isomorphic. We prove the correctness of this transformation by the basic theorem for heterogeneous as well as classical concept lattices.

关键词： basic theorem heterogeneous concept lattice,representation

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On intent stability index for one-sided concept lattices

On intent stability index for one-sided concept lattices

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International Symposium on Applied Computational Intelligence and Informatics ( SACI)

作者： P Butka J. Pócsova J. Pócs Department of Cybernetics and Artificial Intelligence Technical University of Košice Košice Slovakia Institute of Control and Informatization of Production Processes Technical University of Košice Košice Slovakia Mathematical Institute Slovak Academy of Sciences Košice Slovakia Department of Algebra and Geometry Palacký University Olomouc Czech Republic

The intent stability index represents an useful relevancy measure of the extracted patterns in the FCA data mining method. We describe this kind of relevancy measure for the so-called one-sided concept lattices, which represent a fuzzy generalization of the classical FCA. The basic properties of the stability index and some experimental results concerning this index conducted on randomly generated dataset are discussed.

关键词： Stability criteria Lattices Indexes Context Data mining Monte Carlo methods

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On the inverse problem for generalized one-sided concept lattices

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Informatica (Slovenia) 2014年第2期38卷 95-101页

作者： Pócs, Jozef Pócsová, Jana Palacký University Olomouc Department of Algebra and Geometry Olomouc Czech Republic Mathematical Institute Slovak Academy of Sciences Košice Slovakia Technical University of Košice BERG Faculty Institute of Control and Informatization of Production Processes Košice Slovakia

Generalized one-sided concept lattices represent a generalization of the classical concept lattices convenient for analysis of object-attribute models with different types of attributes. Formally, to each objectattribute model (represented by the notion of formal context) there is assigned a pair of concept-forming operators. Fixed points of these operators form a hierarchical structure consisting of extent-intent pairs. From the algebraic point of view this structure forms a complete lattice, called the generalized one-sided concept lattice. In this paper we deal with the inverse problem for generalized one-sided concept lattices. For a given generalized one-sided concept lattice we describe an algorithm for finding the corresponding formal context.

关键词： Inverse problems

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Distributed computation of generalized one-sided concept lattices on sparse data tables

Distributed computation of generalized one-sided concept lat...

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作者： Butka, Peter Pócs, Jozef Pócsová, Jana Department of Cybernetics and Artificial Intelligence Faculty of Electrical Engineering and Informatics Technical University of Košice Letná 9 Košice04200 Slovakia Department of Algebra and Geometry Palacký University Olomouc 17. Listopadu 12 Olomouc77146 Czech Republic Mathematical Institute Slovak Academy of Sciences Grešákova 6 Košice04001 Slovakia BERG Faculty Institute of Control and Informatization of Production Processes Technical University of Košice Boženy Němcovej 3 Košice04384 Slovakia

In this paper we present the study on the usage of distributed version of the algorithm for generalized one-sided concept lattices (GOSCL), which provides a special case for fuzzy version of data analysis approach called formal concept analysis (FCA). The methods of this type create the conceptual model of the input data based on the theory of concept lattices and were successfully applied in several domains. GOSCL is able to create one-sided concept lattices for data tables with different attribute types processed as fuzzy sets. One of the problems with the creation of FCA-based models is their computational complexity. In order to reduce the computation times, we have designed the distributed version of the algorithm for GOSCL. The algorithm is able to work well especially for data where the number of newly generated concepts is reduced, i.e., for sparse input data tables which are often used in domains like text-mining and information retrieval. Therefore, we present the experimental results on sparse data tables in order to show the applicability of the algorithm on the generated data and the selected text-mining datasets.

关键词： Formal concept analysis

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Reduction of concepts from generalized one-sided concept lattice based on subsets quality measure

Advances in Intelligent Systems and Computing

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Advances in Intelligent Systems and Computing 2015年 314卷 101-111页

作者： Butka, Peter Pócs, Jozef Pócsová, Jana Technical University of Košice Department of Cybernetics and Artificial Intelligence Letná 9 Košice04200 Slovakia Palacký University Olomouc Department of Algebra and Geometry 17. listopadu 12 Olomouc771 46 Czech Republic Mathematical Institute Slovak Academy of Sciences Grešákova 6 Košice040 01 Slovakia Technical University of Košice Institute of Control and Informatization of Production Processes Boženy Němcovej 3 Košice043 84 Slovakia

One of the conceptual methods in data mining area is based on the one sided concept lattices, which belongs to approaches known as Formal Concept Analysis (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. © Springer International Publishing Switzerland 2015.

关键词： Formal concept analysis

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Multicriterial analysis of factors considering intensity and extent of floods

Multicriterial analysis of factors considering intensity and...

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15th International Carpathian control Conference, ICCC 2014

作者： Pauliková, Alena Železník, Ondrej Department of Environmentalistics Institute of Safety Quality and Environmental Science Technical University of Košice Park Komenského 5 04187 Košice Slovakia Technical University of Košice Faculty of Mining Ecology Process Control and Geotechnology Institute of Control and Informatization of Production Processes Boženy Němcovej 3 042 00 Košice Slovakia

ISBN: (纸本)9781479935284

Analysis of factors is important in view of the implementation of flood protection remedial measures. A comprehensive solution is possible if at the beginning there are all the relevant factors in detail characterized predominately that have got a major impact on the area in terms of flood risk and flood prevention. Three main groups of soil factors fall into their layout, forest and agricultural. These factors can be evaluated by means of a supplementary tool, e.g. multi-criteria analysis, which improves and supports decision processes in the framework of municipal government management, etc. © 2014 IEEE.

关键词： Floods

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Bisection-based merging algorithm for creation of one-sided concept lattices

Bisection-based merging algorithm for creation of one-sided ...

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International Symposium on Applied Machine Intelligence and Informatics (SAMI)

作者： P. Butka J. Pócsova J. Pócs Department of Cybernetics and Artificial Intelligence Faculty of Electrical Engineering and Informatics Technical University of Košice Košice Slovakia Institute of Control and Informatization of Production Processes BERG Faculty Technical University of Košice Košice Slovakia Department of Algebra and Geometry Faculty of Science Palacký University Olomouc Olomouc Czech Republic

In this paper we provide the new version of algorithm for creation model called Generalized One-Sided Concept Lattice (GOSCL). This model provides the specific fuzzy version of data analytical method based on the approach known as Formal Concept Analysis (FCA), which supports data tables containing the multiple types of attributes defined as fuzzy sets. The acquisition of the FCA models is computationally complex task and it is important to find more effective algorithms for their creation. Therefore, we have designed the algorithm for the reduction of the computation times, which is based on the simple division of input data table using bisection-based approach and then merging procedure compose the local models into one finally merged concept lattice for the complete input data. We present the illustrative experiments which prove the applicability of the presented algorithm for sparse data inputs, where it is possible to get significant decrease of computation times. More effective algorithm for sparse data can be useful for the application of FCA-based models in sparse domains like information retrieval or text analysis.

关键词： Lattices Merging Context Data models Partitioning algorithms Algorithm design and analysis Computational modeling

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