The paper presents learning algorithms for a multidimensional adaptive growing neuro-fuzzy system with optimization of a neuron ensemble in every cascade. A building block for this architecture is a multidimensional neo-fuzzy neuron. The demonstrated system is distinguished from the well-recognized cascade systems in its ability to handle multidimensional data sequences in an online fashion, which makes it possible to treat non-stationary stochastic and chaotic data with the demanded accuracy. The most important privilege of the considered hybr...