Jozef Pócs - Academia.edu (original) (raw)

Papers by Jozef Pócs

Information Sciences, 2015

The main aim of this paper is to introduce the preference relations on generalized onesided conce... more The main aim of this paper is to introduce the preference relations on generalized onesided 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.

ABSTRACT In this paper we provide the new version of algorithm for creation model called Generali... more ABSTRACT 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.

Mathematica Slovaca, 2012

For a monounary algebra (A, f ) we denote R ∅ (A, f ) the system of all retracts (together with t... more For a monounary algebra (A, f ) we denote R ∅ (A, f ) the system of all retracts (together with the empty set) of (A, f ) ordered by inclusion. This system forms a lattice. We prove that if (A, f ) is a connected monounary algebra and R ∅ (A, f ) is finite, then this lattice contains no diamond. Next distributivity of R ∅ (A, f ) is studied. We find a representation of a certain class of finite distributive lattices as retract lattices of monounary algebras. c 2012 Mathematical Institute Slovak Academy of Sciences 2010 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 08A60. K e y w o r d s: monounary algebra, retract, lattice of retracts.

Mathematica Slovaca, 2011

We investigate lattices of retracts of monounary algebras. Semimodularity and concepts related to... more We investigate lattices of retracts of monounary algebras. Semimodularity and concepts related to semimodularity (M-symmetry and Mac Lane's condition) are dealt with. Further, we give a description of all connected monounary algebras with modular retract lattice. c 2011 Mathematical Institute Slovak Academy of Sciences 2000 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 08A60. K e y w o r d s: monounary algebra, retract, lattice of retracts.

Journal of Applied Mathematics, 2013

Information Sciences, 2014

The methods of conceptual scaling and generalized one-sided concept lattices represent different ... more 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.

Czechoslovak Mathematical Journal, 2008