The method of multidimensional analysis and forecasting states of complex systems and processes based on Fuzzy Cognitive Temporal Models
Problem definition. The limitations of existing models and methods for multidimensional analysis and prediction of the state of complex systems and processes is the difficulty of taking into account the indirect effect of interdependent components in the face of uncertainty. Other, no less significant problems are: non-linear nature of the interaction of objects and processes; lack of consistency; diverse quality, insufficient volume, incompleteness and inconsistency of information about objects and processes in such systems and their influence on each other. It is required to propose a method for multivariate analysis and prediction of the state of complex systems and processes, providing multivariate analysis and accounting for the direct and indirect interference of all components of multidimensional time series with their different time lags relative to each other, as well as their predictive assessment under conditions of non-stochastic uncertainty, non-linear interaction, partial inconsistencies and significant interdependence of components of multidimensional time series. The aim of the work is to develop a method that improves the accuracy of multidimensional prediction of the state of complex systems and processes. Methods used : forecasting multidimensional time series; fuzzy cognitive analysis and modeling; fuzzy sets and calculations; fuzzy logic inference; mathematical statistics. Novelty: A new type of Fuzzy Cognitive Temporal Models is proposed, consisting of many concepts that are connected by subsets of fuzzy degrees of influence, ordered in chronological order, taking into account the time lags of the corresponding components of a multidimensional time series. To implement fuzzy temporal transformations of concepts, the proposed Fuzzy Component Temporal Models are used, which are modified ANFIS-type models, and provide the formation, storage and output of the predicted fuzzy values of the corresponding components of the multidimensional time series with the time delays required for the Fuzzy Cognitive Temporal Model. An original approach is presented and a method of structurally-parametric tuning of a Fuzzy Cognitive Temporal Model of the proposed type is implemented, which includes: firstly, preliminary structural tuning of a Fuzzy Cognitive Temporal Model; secondly, the training of each Fuzzy Component Temporal Model of the Fuzzy Cognitive Temporal Model; thirdly, the coordination of all Fuzzy Component Temporal Models of the Fuzzy Cognitive Temporal Model to ensure the maximum increase in the forecast accuracy of each component of the multidimensional time series without compromising the accuracy of prediction of at least one of the other components of the multidimensional time series. A new method has been developed for multidimensional analysis and prediction of the state of complex systems and processes based on a new type of Fuzzy Cognitive Temporal Model that provides multidimensional analysis and consideration of the direct and indirect interference of all components of a multidimensional time series with their different time lags relative to each other, as well as their predictive assessment in conditions of non-stochastic uncertainty, non-linearity of mutual influence, partial inconsistency and significant interdependence of components multidimensional time series. Various modes of using the developed method are described. Result: the proposed method was used to solve the problem of multidimensional forecasting the sustainability of the urban environment of Moscow. Practical significance: the method proposed in the article allows, in small samples, to increase the accuracy of multivariate analysis and forecasting of complex systems and processes (using multidimensional forecasting of the stability of the urban environment of Moscow) by an average of 10-15% compared to the neural network approach, which demonstrated some of the best results when solving this problem. The forecasting for the sustainability of the urban environment of Moscow was made without taking of the effect of coronavirus infection on it. At the same time, it is obvious that the use of the proposed original method is very popular in the current difficult conditions and allows us to provide reliable analysis and multidimensional forecasting of the stability of the urban environment in different regions both in Russia and in other countries, especially taking into account the complex epidemiological situation.