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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2021-25-3-70-85</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-925</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Информатика, вычислительная техника и управление</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Computer science, computer engineering and IT managment</subject></subj-group></article-categories><title-group><article-title>Исследование устойчивости нейро-нечёткой системы вывода, основанной на методе отношения площадей</article-title><trans-title-group xml:lang="en"><trans-title>Stability Study of a Neuro-Fuzzy Output System Based on Ratio Area Method</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3779-9165</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Милостная</surname><given-names>Н. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Milostnaya</surname><given-names>N. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Милостная Наталья Анатольевна, кандидат технических наук</p><p>ул. 50 лет Октября, д. 94, г. Курск 305040</p></bio><bio xml:lang="en"><p>Natalya A. Milostnaya, Cand. of Sci. (Engineering)</p><p>50 Let Oktyabrya str. 94, Kursk 305040</p></bio><email xlink:type="simple">nat_mil@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Юго-Западный государственный университет</institution></aff><aff xml:lang="en"><institution>Southwest State University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>29</day><month>01</month><year>2022</year></pub-date><volume>25</volume><issue>3</issue><fpage>70</fpage><lpage>85</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Милостная Н.А., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Милостная Н.А.</copyright-holder><copyright-holder xml:lang="en">Milostnaya N.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://izvestswsu.elpub.ru/jour/article/view/925">https://izvestswsu.elpub.ru/jour/article/view/925</self-uri><abstract><p>Цель исследования: исследование гипотезы о возможности изменения вида переходного процесса во время обучения нейро-нечёткой системы вывода, основанной на методе соотношения площадей, и изучения свойств влияния весового коэффициента на её устойчивость.Методы. Для разработки нейро-нечёткой системы вывода в статье используется аппарат нечёткой логики. При этом входные и выходные переменные описываются треугольными функциями принадлежности, в композиционном правиле использовалась модель импликации Мамдани. При дефаззификации применялась линейная модель отношения площадей. Во время обучения использовался метод обратного распространения ошибки.Результаты. В ходе экспериментальных исследований было установлено, что предложенная нейро-нечёткая модель, основанная на методе отношения площадей, позволяет изменять вид переходного процесса, а именно преобразовать колебательный процесс в апериодический (монотонный) процесс. Также в ходе экспериментальных исследований было установлено, что на устойчивость нейро-нечёткой системы вывода в большей степени влияет весовой коэффициент, определяемый при расчете общей площади выходных функций принадлежности. Таким образом, полученные результаты доказывают: во-первых, что предложенная нейро-нечёткая система вывода обеспечивает трансформацию передаточных характеристик, а во-вторых, обеспечивает её устойчивость в заданном диапазоне характеристик весового коэффициента.Заключение. В статье представлена архитектура адаптивной нейро-нечёткой системы вывода, основанной на линейном методе отношения площадей. Отличительной особенностью предлагаемой архитектуры является использование на входах и выходе нечёткой системы треугольных функций принадлежности. Анализ имитационного процесса её обучения показал, что при обучении с целью обеспечения устойчивости необходимо устанавливать допустимые значения весового коэффициента, численные значения которого, в свою очередь, влияют на трансформацию передаточных характеристик нейро-нечёткой системы вывода. </p></abstract><trans-abstract xml:lang="en"><p>Purpose of research is to study the hypothesis about the possibility of changing the type of transition process during training in a neuro-fuzzy inference system based on area ratio method, and to study the properties of weight coefficient influence on its stability.Methods. An apparatus of fuzzy logic is used for the development of a neuro-fuzzy output system. At the same time, input and output variables are described by triangular membership functions. Mamdani implication model was used in the compositional rule. A linear model of area ratio was used in defasification. The reverse error propagation method was used during training.Results. In experimental studies, it was found that the proposed neuro-fuzzy model based on area ratio method allows to change the type of transition process, namely, to transform oscillatory process into an aperiodic (monotonic) process. In experimental studies, it was also found that the stability of neuro-fuzzy output system is more influenced by the weight coefficient determined in calculating the total area of membership output functions. Thus, the obtained results prove: first, that the proposed neuro-odd output system ensures the transformation of transfer characteristics, and second, ensures its stability in a given range of weight coefficient characteristics.Conclusion: The architecture of an adaptive neuro-fuzzy output system based on a linear method of area ratio is described. A distinctive feature of the proposed architecture is the use of an odd system of triangular accessory functions at inputs and outputs. Analysis of the simulation process of its training showed that it s important to ensure stability during training. It is also necessary to establish permissible values of the weight coefficient, numerical values of which in its turn affect the transformation of transfer characteristics of a neuro-fuzzy output system.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>адаптивная нейро-нечёткая система вывода</kwd><kwd>метод отношения площадей</kwd><kwd>обучение</kwd><kwd>устойчивость</kwd></kwd-group><kwd-group xml:lang="en"><kwd>adaptive neuro-fuzzy output system</kwd><kwd>area ratio method</kwd><kwd>training</kwd><kwd>sustainability</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена в рамках государственного задания ГЗ № 0851-2020-0032.</funding-statement><funding-statement xml:lang="en">Work carried out within the framework of the state law № 0851-2020-0032.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Shahmoradi S., Shouraki S.B. 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