Methods of searching for the Kemeny median for non-strict and partial orderings of alternatives

Калач Андрей Владимирович – доктор химических наук, профессор, заведующий кафедрой информационных технологий, моделирования и управления, Воронежский государственный университет инженерных технологий, г. Воронеж, Российская Федерация, ORCID iD: https://orcid.org/0000-0002-8926-3151, e-mail: [email protected]. Бугаев Юрий Владимирович – доктор физико-математических наук, профессор, профессор кафедры информационных технологий, моделирования и управления, Воронежский государственный университет инженерных технологий, г. Воронеж, Российская Федерация, ORCID iD: https://orcid.org/0000-0002-1043-7682, e-mail: [email protected]. Никитин Борис Егорович – кандидат физико-математических наук, доцент, профессор кафедры информационных технологий, моделирования и управления, Воронежский государственный университет инженерных технологий, г. Воронеж, Российская Федерация, ORCID iD: https://orcid.org/0000-0002-6508-8723, e-mail: [email protected]. Kalach Andrey Vladimirovich is Dr. Sc. (Chemistry), Professor, Head of the Department of Infor-mation Technology, Modeling and Management, Voronezh State University of Engineering Technolo-gies, Voronezh, Russian Federation, ORCID iD: https://orcid.org/0000-0002-8926-3151, e-mail: [email protected]. Bugaev Yuriy Vladimirovich is Dr. Sc. (Physics and Mathematics), Professor, Department of In-formation Technology, Modeling and Management, Voronezh State University of Engineering Technol-ogies, Voronezh, Russian Federation, ORCID iD: https://orcid.org/0000-0002-1043-7682, e-mail: [email protected]. Nikitin Boris Egorovich is Cand. Sc. (Physics and Mathematics), Associate Professor, Department of Information Technology, Modeling and Management, Voronezh State University of Engineering Technologies, Voronezh, Russian Federation, ORCID iD: https://orcid.org/0000-0002-6508-8723, e-mail: [email protected].В рамках развития подходов к моделированию процессов, лежащих в основе принятия решений во всех сферах человеческой деятельности, приведено описание разработанного приближенного алгоритма на-хождения медианы Кемени для набора нестрогих упорядочений альтернатив. Исследование осуществляли в рамках современной методологии выбора альтернатив, которая предполагает выбор обоснованного решения по окончании анализа и обобщения поступающей информации и достижения некоторого заданного порогового значения величины критерия принятия решения. Предложено обоснование выбора вариантов решений многокритериальных задач в сфере планирования и управления из существующего множества альтернатив с использованием экспертных оценок. В рамках современной методологии выбора альтернатив предложены два алгоритма поиска медианы Кемени при наличии нестрогих и частичных упорядочений в исходном профиле, а также при наличии альтернатив, не оцененных экспертами. Рассмотрены особенности построения медианы Кемени по предлагаемому алгоритму на конкретном численном примере. Показана обосно-ванность использования разработанного приближенного алгоритма для решения экспрессного по сравнению с традиционным точным алгоритмом. Отдельно отмечено, что в случае наличия нескольких решений алгоритм гарантирует нахождения варианта, достаточно близкого к какому-нибудь экспертному упорядочению рассматриваемого профиля экспертных оценок. This article describes an approximate algorithm for finding the Kemeny median for a set of non-strict orderings of alternatives. The study was carried out for choosing alternatives involving making an informed decision on the completion of the analysis and generalization of incoming information and reaching a threshold value for the decision criterion. The article offers a justification for choosing solutions to multi-criteria tasks in planning and management from an existing set of alternatives using expert assessments. Two algorithms for searching for the Kemeny median are proposed in the presence of non-strict and partial orderings in the initial profile and in the presence of alternatives that have not been evaluated by experts. The article discusses constructing the Kemeny median according to the algorithm using a numerical example. The article shows the validity of using the approximate algorithm to solve the express algorithm in comparison with the traditional exact algorithm. It is sepa-rately noted that in the case of several solutions, the algorithm guarantees finding an option that is close enough to an expert ordering of the expert assessment profile under consideration

Human respiratory monitoring during sleep using a two-channel bioradar

permanent sleep deprivation and a decrease in sleep quality. Currently, in clinical practice, the method of polysomnography is used to detect sleep disorders. This method is expensive, labor and time-consuming, as well as uncomfortable for the patient. Therefore, at present, the problem of creating accurate, reliable and comfortable for the patients methods for assessing the sleep quality, as well as identifying and monitoring various sleep disorders, remains an up-to-date task of modern biomedical engineering. One of these methods is bioradiolocation, which allows detecting sleep disorders based on the variability of the breathing pattern of a sleeping person. However, because the amplitude of chest movements during breathing in different directions differs by an order of magnitude, the quality of the signal received by the bioradar during sleep also varies depending on the orientation of the sleeping person relative to the bioradar. To overcome this problem, in this article we propose a combined use of two bioradars oriented at different angles towards to the sleeping person. Thus, the aim of this work was to develop a bioradar system that provides reliable registration of the breathing pattern for various positions of a sleeping person. During the experiments, we used two monochromatic bioradars "BioRASCAN-24" with probing frequencies in the range of 24.0 and 24.1 GHz, located at an angle of 90 ° to each other. In this work, we used bioradar data recorded for seven volunteers who underwent polysomnographic research at the sleep laboratory of Almazov National Medical Research Centre. During the night, a parallel recording of bioradar signals and polysomnographic data was carried out for each subject using the Embla N7000 system (Natus Neurology Inc., USA). The duration of the experimental recording for each subject was from 7 to 9 hours. An algorithm was developed to extract a breathing pattern from a bioradar signal and estimate the respiratory rate of a sleeping person. It consisted of the following stages: synchronization of the bioradar and polysomnographic signals, demodulation, exclusion from consideration of signal fragments containing motion artifacts, signal filtering in order to isolate the breathing pattern, assessment of respiration rate in the inter-artifact periods for each of the bioradars separately, the final estimation of the respiration rate for the inter-artifact periods, taking into account the combination of data for both radars. Bioradar signal processing algorithms were done utilizing Matlab 2020b. To assess the accuracy of the proposed algorithm, we compared the respiratory rates calculated for each 30-second epoch using bioradar data with similar parameters calculated by the abdominal belt polysomnography sensor. The efficiency of the proposed algorithm was estimated by the accuracy and the mean absolute error. The results obtained for seven volunteers showed that the developed two-channel bioradar system turned out to be more accurate and reliable than a single bioradar. In the course of further research, it is planned to expand the dataset to include data from volunteers not only with sleep-related breathing disorders, but also with other sleep disorders. Although this work was carried out with the involvement of only seven volunteers, it is nevertheless an important step towards the development of a reliable view-independent bioradar system for assessing breathing rate during sleep.</jats:p