Abstract-One of the typical important criteria to be considered in real-time control applications is the computational complexity of the controllers, observers, and models applied. In this paper, a singular value decomposition (SVD)-based complexity reduction technique is proposed for Takagi Sugeno (TS) fuzzy models. The main motivation is that the TS fuzzy model has exponentially growing computational complexity with the improvement of its approximation property through, as usually practiced, increasing the density of antecedent terms. The reduction technique proposed here is capable of defining the contribution of each local linear model included in the TS fuzzy model, which serves to remove the weakly contributing ones as according to a given threshold. Reducing the number of models leads directly to the computational complexity reduction. This work also includes a number of numerical and application examples.

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This article aims to propose a methodological framework to determine the degree of the dynamic impact of the effect of activities in the field of sustainable waste logistics on the development of trade in recyclable raw materials in the chosen countries of the European Union, especially in Poland and Hungary. In order to determine the dynamic interdependence between the indicated phenomena, econometric tools associated with the vector autoregression model were used, namely: Granger causality tests, impulse response function and variance decomposition of forecast errors. The tools used will not only identify the direction of the causal interdependence between the effects of sustainable logistics activities and the development of trade in recyclable raw materials, but also allow to determine the strength of the interaction between these variables. The conducted research shows that changes in the environmental effects of waste logistics activities are the Granger cause of changes occurring in the trade of renewable raw materials, especially in Hungary. Considering adequately delayed values of the synthetic development measure of the environmental effects of waste logistics increases the accuracy of predictions for changes in the trade of recyclable raw materials.

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