Neuro-Fuzzy Cognitive Temporal Models For Predicting Multidimensional Time Series With Fuzzy Trends

Abstract

A new type of Neuro-Fuzzy Cognitive Temporal Models (NFCTM) is proposed for predicting multidimensional time series (MTS) taking into account the fuzzy trends of all MTS components. NFCTMS allow predicting the MTS in conditions of non-stochastic uncertainty, non-linearity of mutual influence, partial inconsistency and significant interdependence of the MTS components, as well as in conditions of small samples. This takes into account the direct and indirect mutual influence of all the MTS components with different time lags relative to each other. To carry out temporal changes in specific MTS components the original neuro-fuzzy models of RecANFIS (Recurrent Adaptive Neuro-Fuzzy Inference System/Model) type are applied, that: firstly, allow to save the predicted values of the MTS components in the range of “liding-window” time series; secondly, identify fuzzy trends of the components of the MTS in the range of “sliding-window” time series; thirdly, adaptively take into account fuzzy trends of the MTS components based on the fuzzy mappings. An original way of a coherent learning NFCTM is described, which lies: firstly, in training RecANFISs for each concept NFCTM (MTS component) taking into account fuzzy trends; secondly, in coherence of all RecANFISs between each other to maximize the prediction accuracy of each of the MTS components without compromising the prediction accuracy of at least one of the other MTS components. Experimental studies have been carried out and the results of using the proposed NFCTM for multidimensional forecasting of the urban environment state in Moscow in conditions of a complex epidemiological situation have been obtained.