Research Article
Ontology of Mathematical Modeling Based on Interval Data
Mykola Dyvak ,
1
Andriy Melnyk ,
1
Artur Rot ,
2
Marcin Hernes ,
2
and Andriy Pukas
1
1
Department of Computer Science, West Ukrainian National University, 11 Lvivs’ka Str., Ternopil 46000, Ukraine
2
Faculty of Management, Wroclaw University of Economics and Business, Komandorska 118/120, Wroclaw 53-345, Poland
Correspondence should be addressed to Andriy Melnyk; melnyk.andriy@gmail.com
Received 8 February 2022; Revised 9 April 2022; Accepted 13 June 2022; Published 19 July 2022
Academic Editor: Andrea Murari
Copyright©2022MykolaDyvaketal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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. is 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. e 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.
1. Introduction
Mathematical modeling is one of the main tools that allows
describing the object in a simple form, exploring it, and
predicting behavior. Mathematical modeling is understood
as the process of building a model and its application to
certain applied problems [1–4].
Mathematical modeling processes consist of a large number
of procedures, which are mainly implemented in the relevant
tools, that is, in the form of certain software systems [3, 4].
Examples of these software environments are Matlab,
GNU Octave, Scilab, and SageMath. ese tools are mul-
tipurpose and well developed. However, practitioners often
need to use more specialized tools for building mathematical
models, as well as to adapt existing tools to nonstandard
conditions that are absent in the noted environments. In this
case, there are difficulties in using and interpreting such
tools because the simulation procedures are hidden from the
researcher, and this makes it difficult to use them by making
appropriate software changes [4–8].
In this case, the most appropriate solution is to create an
ontological description of certain methods of mathematical
modeling. It describes in detail the components of a model
building process and its application. en this ontological
description is used to generate appropriate software. is
approach, on the one hand, will allow the integration of the
created software in various applied systems and, on the other
hand, will make changes to existing software [4, 9–12].
e availability of ontological descriptions of modeling
processes based on certain methods makes it possible to
unify the software used for a wide range of tasks. It enables,
based on experience, a repository of mathematical model
creation that can be used to model a wide range of math-
ematically similar properties [13–23].
e positive effect of this approach will be a significant
simplification of the process of creating tools for both the
modeling processes organization and their application to
applied problems.
One of the directions of mathematical modeling is the
inductive approach, which is based on a self-organized process
Hindawi
Complexity
Volume 2022, Article ID 8062969, 19 pages
https://doi.org/10.1155/2022/8062969