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PhD. Topics

Mathematical Institute

Topic
Aggregation on lattices
PhD. program
9–1–9 Applied Mathematics
Name of the supervisor
Mgr. Andrea Zemánková, PhD.
Contact:
Receiving school
Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava
Annotation
The theory of aggregation focuses on the expression of complex data in a concise form, usually using a small group of representatives that best characterize the most important properties and structure of the given data, as working with the whole data set is usually very
time-consuming and computationally demanding.

The majority of well-known aggregation methods focus mainly on subsets of real numbers, most often on the unit interval. Recently, the need to work on more complex structures has emerged, as some applications
do not allow the data to be transformed into chains of values and require the presence of incomparable values. Therefore, aggregation on lattices and partially ordered sets is currently in the center of attention, focusing mainly on the modification of classical and the design of new methods for aggregation on such structures.

The aim of the work will be to investigate aggregation functions on
lattices, to study the basic properties of aggregation and their
modification required by applications. The expected outcome will be
the results concerning the construction, characterization and
representation of aggregation functions on lattices.