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.

New criterion and method for design of experiments for two types of tasks of creation of decision support interval model are described. The first type is the tasks of control of permissible values of characteristics of technical, economic, ecological and other static systems. Second type of tasks - it is the tasks of choice of optimum decisions by the criterion of minimization or maximization of value of objective function.

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 methods of the tolerance ellipsoidal estimation for the tasks of synthesis of the tolerances to parameters of radio-electronic circuits and possibility of its parallelization are considered. These methods are the result of the task of estimation the solutions of an interval system of linear algebraic equations (ISLAE) which is built according to given criteria of optimality. The numerical algorithm is proposed for solving the tolerance ellipsoidal estimation tasks with a possibility of parallelization.

In this paper the software system for constructing the mathematical macromodels for objects with distributed parameters using different methods of structure and parameters identification is considered.

The method of structure identification of interval difference operators, based on principles of the bee colonies functioning is represented. An example of the implementation of method for modeling of atmosphere pollution by harmful vehicle emissions is considered.