Number: VEGA 1/0198/09
Period: 1.1.2009-31.12.2011
Principal investigator: Prof. RNDr. Anna Kolesárová, CSc.
Scientific co-workers:
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.
Goals:
Keywords: Aggregation function, extension, fuzzy measure, fuzzy integral, fuzzy nearness and similarity relations, generalized many-valued algebras
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 ordered monoids.