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.

In the paper the problem of structure identification of interval difference operator as a model of distributed parameters object has been considered. For solving this problem was founded mathematical and algorithmic maintenance for method of structure identification, which is based on the algorithm of artificial bee colony.

In the paper, the method of parametric identification of interval discrete dynamic models is considered. An improved scheme of the computational implementation of this method is proposed. The scheme considers an area of permissible values for modeled characteristics. Results of the comparative analysis of the proposed scheme efficiency of this method with a known one are presented.

In the paper, the mathematical model in form of the interval difference operator (IDO) is considered. The model was used for visualization and identification of the recurrent laryngeal nerve on the tissue of the surgery wound. A method for structure identification of the IDO is proposed.

In the paper the modified artificial bee colony algorithm for structure identification of models of objects with distributed parameters and control has been considered. An example of applying the method for identifying the model of drywall drying process in the final phase of its production taking into account various temperature modes of the drying oven is shown.

In this paper the new method of tolerance estimation of parameters set of interval model "input-output" of the static system is created, which allows to base configuration of parameters set, provides greater coverage of domain of parameters of interval model and at the same time differs low calculable complication.