14 citations · 56 across the 15 of their papers we have counts for
15 papers
Closure structures parameterized by systems of isotone Galois connections
Vilem Vychodil
We study properties of classes of closure operators and closure systems parameterized by systems of isotone Galois connections. The parameterizations express stronger requirements…
Invariance to ordinal transformations in rank-aware databases
Vilem Vychodil
We study influence of ordinal transformations on results of queries in rank-aware databases which derive their operations with ranked relations from totally ordered structures of s…
Computing sets of graded attribute implications with witnessed non-redundancy
Vilem Vychodil
In this paper we extend our previous results on sets of graded attribute implications with witnessed non-redundancy. We assume finite residuated lattices as structures of truth deg…
Relational Division in Rank-Aware Databases
Ondrej Vaverka, Vilem Vychodil
We present a survey of existing approaches to relational division in rank-aware databases, discuss issues of the present approaches, and outline generalizations of several types of…
On sets of graded attribute implications with witnessed non-redundancy
Vilem Vychodil
We study properties of particular non-redundant sets of if-then rules describing dependencies between graded attributes. We introduce notions of saturation and witnessed non-redund…
Rational fuzzy attribute logic
Vilem Vychodil
We present a logic for reasoning with if-then formulas which involve constants for rational truth degrees from the unit interval. We introduce graded semantic and syntactic entailm…
Logic of temporal attribute implications
Jan Triska, Vilem Vychodil
We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic ent…
Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections
Vilem Vychodil
We study the semantics of fuzzy if-then rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependencies between fuz…
Monoidal functional dependencies
Vilem Vychodil
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete resi…
Fuzzy inequational logic
Vilem Vychodil
We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formul…
Variety theorem for algebras with fuzzy order
Vilem Vychodil
We present generalization of the Bloom variety theorem of ordered algebras in fuzzy setting. We introduce algebras with fuzzy orders which consist of sets of functions which are co…
On minimal sets of graded attribute implications
Vilem Vychodil
We explore the structure of non-redundant and minimal sets consisting of graded if-then rules. The rules serve as graded attribute implications in object-attribute incidence data a…
Attribute Dependencies for Data with Grades
Radim Belohlavek, Vilem Vychodil
This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the cl…
Discovery of factors in matrices with grades
Radim Belohlavek, Vilem Vychodil
We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes rep…
Sensitivity Analysis for Declarative Relational Query Languages with Ordinal Ranks
Radim Belohlavek, Lucie Urbanova, Vilem Vychodil
We present sensitivity analysis for results of query executions in a relational model of data extended by ordinal ranks. The underlying model of data results from the ordinary Codd…