Title: Conjunctive aggregation operators
Number: VEGA 1/3012/06
Period: 1.1.2006-31.12.2008
Principal investigator: Prof. RNDr. A. Kolesárová, CSc.
Scientific co-workers: Ing. P. Sarkoci (2006-2007), Ing. D. Zelisková (2006), Doc. RNDr. P.Volauf, CSc. (FEI), Doc. RNDr. J. Dobrakovová , CSc. (SjF), Doc. RNDr. M. Kalina, CSc. (SvF), Mgr. J. Mordelová, PhD. (SvF)
Goals:
Keywords:
Aggregation operator, copula, quasi-copula, triangular norm, dominantion, fuzzy topology
Anotation:
Construction of 1-Lipschitz aggregation operators or their best possible bounds from partial information on subdomains. Results in special classes of 1-Lipschitz aggregation operators, including quasi-copulas and copulas. Study of more dimensional cases. Introducing discrete copulas and a deep investigation of their properties, structure and possible applications in mathematical statistics and stochastic processes. Proposal of a method for identification of copulas from observed data, including a software program, and application of obtained results for investigation of the dependence structure of random variables. Study of the relationship between properties of copulas and various measures of association of stochastic variables. Investigation of the domination of triangular norms and general aggregation operators. Application of aggregation operators and dominance for building topologies based on fuzzy nearness relations in environment of logical uncertainty.