Number: VEGA 1/0198/09
Principal investigator: Prof. RNDr. Anna Kolesárová, CSc.
RNDr. Milan Jasem, CSc., Doc. RNDr. P. Volauf, CSc., FEI STU; Doc. RNDr. J. Dobrakovová, CSc., Mgr. A. Stupňanová, PhD., SvF STU; Mgr. J. Mordelová, PhD., SvF STU.
aggregation functions from a partially given information on an
aggregation process. Especially, aggregation functions used in
probability and statistics, in applications of fuzzy logic in
inference processes and in multicriteria decision making.
Completion of a
partially given information on an aggregation process by means of
various types of fuzzy integrals, primarily, by means of the level
dependent Choquet and Sugeno integrals, but also by generalized
fuzzy integrals based on pseudo-operations.
construction of fuzzy nearness and similarity relations by means of
aggregation functions, investigation of relationships between
various types of fuzzy relations and examination of their
Investigation in the
area of generalized MV-algebras and lattice ordered monoids.
Keywords: Aggregation function, extension, fuzzy measure,
fuzzy integral, fuzzy nearness and similarity relations, generalized
Anotation: The extensions of various types of aggregation
functions from a partially given information on subsets of the
domain, and construction of the best possible bounds under given
conditions, especially in the case of copulas, quasi-copulas and
semi-copulas. A detailed examination of properties of the Choquet and
Sugeno integrals defined with respect to level dependent fuzzy
measures and proposals of new types of generalized fuzzy integrals
with respect to level dependent fuzzy measures. Completion of a
partial information on an aggregation process by fuzzy integrals.
Definition of utility functions by means of generalized level
dependent integrals enabling building preference structures and
orderings of considered alternatives. The study and construction of
fuzzy nearness and similarity relations based on new aggregation
techniques. Investigation in the area of MV-algebras and lattice