The aim of this study is to show that the integration of two soft computing techniques, namely the F-transform and fuzzy tendency modeling, can be successfully used in the analysis and forecasting of time series. The proposed method is based on the two-term additive decomposition of a time series, in which the first term is a low-frequency trend (expressed using direct F-transform components), and the second term is a residual vector that is processed as a stationary time series. A theoretical justification is given, and experiments are included. A practical application that shows the analysis of a time series with economic indicators is demonstrated.

The development of the economy and the transition to industry 4.0 creates new challenges for artificial intelligence methods. Such challenges include the processing of large volumes of data, the analysis of various dynamic indicators, the discovery of complex dependencies in the accumulated data, and the forecasting of the state of processes. The main point of this study is the development of a set of analytical and prognostic methods. The methods described in this article based on fuzzy logic, statistic, and time series data mining, because data extracted from dynamic systems are initially incomplete and have a high degree of uncertainty. The ultimate goal of the study is to improve the quality of data analysis in industrial and economic systems. The advantages of the proposed methods are flexibility and orientation to the high interpretability of dynamic data. The high level of the interpretability and interoperability of dynamic data is achieved due to a combination of time series data mining and knowledge base engineering methods. The merging of a set of rules extracted from the time series and knowledge base rules allow for making a forecast in case of insufficiency of the length and nature of the time series. The proposed methods are also based on the summarization of the results of processes modeling for diagnosing technical systems, forecasting of the economic condition of enterprises, and approaches to the technological preparation of production in a multi-productive production program with the application of type 2 fuzzy sets for time series modeling. Intelligent systems based on the proposed methods demonstrate an increase in the quality and stability of their functioning. This article contains a set of experiments to approve this statement.

This article describes solutions to control problems using fuzzy logic, which facilitates the development of decision support systems across various fields. However, addressing this task through the manual creation of rules in specific fields necessitates significant expert knowledge. Machine learning methods can identify hidden patterns. A key novelty of this approach is the algorithm for generating fuzzy rules for a fuzzy controller, derived from interpreting a decision tree. The proposed algorithm allows the quality of the control actions in organizational and technical systems to be enhanced. This article presents an example of generating a set of fuzzy rules through the analysis of a decision tree model. The proposed algorithm allows for the creation of a set of fuzzy rules for constructing fuzzy rule-based systems (FRBSs). Additionally, it autogenerates membership functions and linguistic term labels for all of the input and output parameters. The machine learning model and the FRBS obtained were assessed using the coefficient of determination ($R^2$). The experimental results demonstrated that the constructed FRBS performed on average 2% worse than the original decision tree model. While the quality of the FRBS could be enhanced by optimizing the membership functions, this topic falls outside the scope of the current article.

Data analysis in the context of the features of the problem domain and the dynamics of processes are significant in various industries. Uncertainty modeling based on fuzzy logic allows building approximators for solving a large class of problems. In some cases, type-2 fuzzy sets in the model are used. The article describes constructing fuzzy time series models of the analyzed processes within the context of the problem domain. An algorithm for fuzzy modeling of the time series was developed. A new time series forecasting scheme is proposed. An illustrative example of the time series modeling is presented. The benefits of contextual modeling are demonstrated.

This article studies the approach to solving the problem of controlling the complex organizational and technical systems based on hybrid models. We propose a new component of intelligent decision support that is integrated with control systems. The proposed component is based on fuzzy logic and knowledge engineering. We present a model of ontology to form the context of data analysis and time series modeling. The ontological context allows us to represent trends of the analyzed object indicators. An expert can add a set of fuzzy rules to the ontology for systems control based on the fuzzy inference. The proposed approach allows reducing the time of analysis and interpretation of the results. Experimental results confirm the correctness and effectiveness of the approach proposed in this article.