The paper approaches problem of the flow forecasting for the Liptovska Mara reservoir with a hybrid modelling approach. The nonlinear hybrid modelling framework was investigated under the specific physiographic conditions of the High Core Mountains of Slovakia. The mean monthly flows of rivers used in this study are predominantly fed by snowmelt in the spring and convective precipitation in the summer. Therefore, their hydrological regime exhibits at least two clear seasonal patterns, which provide an intuitive justification for the application of nonlinear regime-switching time series models. Differences in the prevailing geology, orientation of slopes and their exposure to atmospheric circulation for the right and left-sided tributaries of the Vah River indicate that the hydrological regime of mean monthly discharge time series in this area with respect to seasonality and cyclicity may differ, too. Therefore, a simple deterministic water balance scheme was set up for estimating the reservoir inflow from the left and right-sided tributary flows separately. It consists of the linear combination of the measured tributary flows and estimated ungauged tributary flows. The contributions of the ungauged catchments were estimated from flows from gauged tributaries with similar physiographic conditions by weighting these by the ratio of the catchment areas. Separate nonlinear regime-switching time series models were identified for each gauged tributary. The forecasts of the tributaries were combined into a hybrid forecasting model by the water balance model. The performance of the combined forecast, which could better include the specific regime of the time series of tributaries, was compared with the single forecast of the overall reservoir inflow in several combinations. and V štúdii sme porovnávali kvalitu predpovede viacerých lineárnych a nelineárnych modelov časových radov pri predpovedaní prítokov do nádrže Liptovská Mara. Testovali sme výkonnosť modelov ARMA, SETAR na samotnej rieke Váh a v kombinácii jej prítokov do nádrže Liptovská Mara. Ďalej bol uplatnený jednoduchý deterministický model vodnej bilancie pre prítok do nádrže, ktorý pozostáva z lineárnej kombinácie meraných prietokov prítokov Váhu vážených plochou subpovodia. Výber analogónov sa vykonal vzhľadom na podobnosť fyzicko-geografických podmienok v meraných a nemeraných subpovodiach. Modely typu ARMA a SETAR boli zostavené pre každý prítok osobitne a predpovede prietokov na prítokoch boli skombinované modelom vodnej bilancie a do predpovede celkového prítoku do nádrže. Kombinovanú hybridnú predpoveď (stochasticko-deterministická), zachovávajúcu špecifický režim prítokov a vodnej bilancie v povodiach, sme porovnali s predpoveďou celkového prítoku do nádrže získanou pomocou modelov identifikovaných na hlavnom toku.
The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.