An ontological approach as a tool for managing the processes of constructing mathematical models based on interval data and further use of these models for solving applied problems is proposed in this article. Mathematical models built using interval data analysis are quite effective in many applications, as they have “guaranteed” predictive properties, which are determined by the accuracy of experimental data. However, the application of mathematical modeling methods is complicated by the lack of software tools for the implementation of procedures for constructing this type of mathematical models, creating an ontological model that operates by the categories of the subject area of mathematical modeling, regardless of the modeling object proposed in this article. This approach has made it possible to generate tools for mathematical modeling of various objects based on the interval data analysis for any software development environment selected by the user. The technology of creating the software on the basis of the developed ontological superstructure for mathematical modeling using the interval data for different objects, as well as various forms of user interface implementation, is presented in this article. A number of schemes, which illustrate the technology of using the ontological approach of mathematical modeling based on interval data, are presented, and the features of its interpretation when solving environmental monitoring problems are described.

Mathematical models of the efficiency dynamics of information web resources are considered in this paper. The application of interval discrete models in the form of difference equations is substantiated and the approach to estimation of the model parameters is proposed. The proposed approach is based on the artificial bee colony algorithm (ABCA). A number of experimental studies have been carried out based on data on the functioning of web resources related to environmental monitoring services. The indicator of an information web resource user’s activity has been investigated. Three cases of model building in the form of difference equations as interval discrete models (IDM) have been considered. They vary in the general kind of expression. As a result of the computational experiments, it is shown that the adequacy of a model depends on the expression of the difference equation. In the case of its incorrect choice, the proposed method of parameters’ identification may be ineffective. The obtained interval discrete model in the difference equation form, which describes the efficiency of a web resource, makes it possible to optimize business processes in an organization that uses this web resource, as well as optimally allocate organizational resources and the workload of employees of the administrative service center. Based on the conducted experiments, the efficiency of the proposed model’s application is confirmed.

The article deals with the issue of modeling taking into consideration nitrogen dioxide pollution of the atmospheric surface layer caused by vehicle exhaust gases. The interval data analysis methods were suggested. The method of identifying the mathematical model of the distribution of nitrogen dioxide as an atmospheric air pollutant based on the analysis of data with known measurement errors was proposed and grounded for the first time. The obtained mathematical model in the form of a difference equation is characterized by the guaranteed accuracy of forecasting nitrogen dioxide concentrations in a specified area of the city. It also adequately takes into account traffic changes which significantly reduces the costs of environmental control and monitoring. The proposed new model identification method is more effective in terms of computational time complexity compared to the known method and it is based on taking into account measurement errors which in the final case provides predictive properties of the model with guaranteed accuracy.