The effectiveness of high-order Takagi-Sugeno-Kang (TSK) neuro-fuzzy systems is considered. These systems utilize more complex calculations to perform fuzzy inference but produce better precision when compared to regular TSK systems. Better precision is provided by creating a piecewise polynomial approximation system, while classic or first-order TSK systems provide a piecewise linear approximation, which limits the precision. The general approach for high-order TSK-systems implementation is presented. The described approach involves a modification of the ANFIS (Adaptive Neuro-Fuzzy System) defuzzification procedure. Different characteristics of regular and high-order neuro-fuzzy TSK systems are compared with each other to estimate the benefits of developing more complex neuro-fuzzy models. Increasing the TSK-system order produced better approximation precision for the same configuration of fuzzy sets for physical dependencies approximation. The training time of high-order TSK systems and the sizes of produced models were also compared: presented approach can be used as a way to reduce the size of a neuro-fuzzy approximation system. It is possible to achieve similar precision results, while also reducing the system size.