39 citations · 182 across the 24 of their papers we have counts for
27 papers
On Boolean sublattices of finite partition lattices
Foldes Stephan, Sandor Radeleczki
We investigate maximal Boolean sublattices of the partition lattice Part(U) of a finite universe U. First, any largest size Boolean sublattice of Part(U) can be formed using all pa…
Characterising regular double Stone and pseudocomplemented Kleene algebras in completions of rough sets induced by reflexive relations
Jouni Järvinen, Sándor Radeleczki
We consider Kleene and Stone algebras defined on the completion DM(RS) of the ordered set of rough sets induced by a reflexive relation. We focus on the cases where the completion…
Generalized quasiorders: constructions and characterizations
D. Jakubíková-Studenovská, R. Pöschel, S. Radeleczki
Quasiorders have the property that an operation preserves if and only if each (unary) translation obtained from is an endomorp…
The structure of rough sets defined by reflexive relations
Jouni Järvinen, Sándor Radeleczki
For several types of information relations, the induced rough sets system RS does not form a lattice but only a partially ordered set. However, by studying its Dedekind-MacNeille c…
Nelson algebras, residuated lattices and rough sets: A survey
Jouni Järvinen, Sándor Radeleczki, Umberto Rivieccio
Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. De…
On the lattice of fuzzy rough sets
Dávid Gégény, Sándor Radeleczki
By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets wh…
Generalized Quasiorders and the Galois Connection End-gQuord
Danica Jakubíková-Studenovská, Reinhard Pöschel, Sándor Radeleczki
Equivalence relations or, more general, quasiorders (i.e., reflexive and transitive binary relations) have the property that an -ary operation preserves , i.e., i…
Pseudo-Kleene algebras determined by rough sets
Jouni Järvinen, Sándor Radeleczki
We study the pseudo-Kleene algebras of the Dedekind-MacNeille completion of the ordered set of rough set determined by a reflexive relation. We characterize the cases when PBZ and…
Defining rough sets as core-support pairs of three-valued functions
Jouni Järvinen, Sándor Radeleczki
We answer the question what properties a collection of three-valued functions on a set must fulfill so that there exists a quasiorder on such that the…
Algebraic Approach to Directed Rough Sets
Mani A, Sandor Radeleczki
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The…
Notes on the lattice of fuzzy rough sets with crisp reference sets
Dávid Gégény, László Kovács, Sándor Radeleczki
Since the theory of rough sets was introduced by Zdzislaw Pawlak, several approaches have been proposed to combine rough set theory with fuzzy set theory. In this paper, we examine…
The structure of multigranular rough sets
Jouni Järvinen, Sándor Radeleczki
We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called "optimistic" and "pessimistic" multigranular approximation systems are given.…
G. Czédli's tolerance factor lattice construction, and weak ordered relations
Sándor Radeleczki
The main results of the paper points out the connection between the weak ordered relations and factor lattices defined by tolerances. It is proved that for any tolerance of a l…
Defining rough sets using tolerances compatible with an equivalence
Jouni Järvinen, László Kovács, Sándor Radeleczki
We consider tolerances compatible with an equivalence on , meaning that the relational product is included in . We present the essential properties of …
Involutive right-residuated l-groupoids
Ivan Chajda, Sandor Radeleczki
A common generalization of orthomodular lattices and residuated lattices is provided corresponding to bounded lattices with an involution and sectionally extensive mappings. It tur…
Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets
Jouni Järvinen, Sándor Radeleczki
We introduce Kleene-Varlet spaces as partially ordered sets equipped with a polarity satisfying certain additional conditions. By applying Kleene-Varlet spaces, we prove that each…
The meet operation in the imbalance lattice of maximal instantaneous codes: alternative proof of existence
Stephan Foldes, D. Stott Parker, Sandor Radeleczki
An alternative proof is given of the existence of greatest lower bounds in the imbalance order of binary maximal instantaneous codes of a given size. These codes are viewed as maxi…
The lattice of congruence lattices of algebras on a finite set
Danica Jakubíková-Studenovská, Reinhard Pöschel, Sándor Radeleczki
The congruence lattices of all algebras defined on a fixed finite set ordered by inclusion form a finite atomistic lattice . We describe the atoms and coatoms. Each…
Representing regular pseudocomplemented Kleene algebras by tolerance-based rough sets
Jouni Järvinen, Sándor Radeleczki
We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irred…
Tolerances induced by irredundant coverings
Jouni Järvinen, Sándor Radeleczki
In this paper, we consider tolerances induced by irredundant coverings. Each tolerance on determines a quasiorder by setting if and only if $R…
Monteiro spaces and rough sets determined by quasiorder relations: Models for Nelson algebras
Jouni Järvinen, Sándor Radeleczki
Rough sets induced by quasiorders appear in several constructions using binary relations in computer science. In this paper, a structural characterisation of rough sets induced by…
Interval decomposition lattices are balanced
S. Foldes, S. Radeleczki
Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in a linearly ordered set. Join-irreducible partitions into intervals are cha…
Rough sets determined by tolerances
Jouni Järvinen, Sándor Radeleczki
We show that for any tolerance on , the ordered sets of lower and upper rough approximations determined by form ortholattices. These ortholattices are completely distrib…
A general framework for island systems
Stephan Foldes, Eszter K. Horváth, Sándor Radeleczki +1
The notion of an island defined on a rectangular board is an elementary combinatorial concept that occurred first in [G. Czédli, The number of rectangular islands by means of distr…