Кафедра "Комп'ютерна математика і аналіз даних"

Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/7570

Офіційний сайт кафедри http://web.kpi.kharkov.ua/kmmm

Кафедра "Комп'ютерна математика і аналіз даних" заснована в 2002 році.

Кафедра входить до складу Навчально-наукового інституту комп'ютерних наук та інформаційних технологій Національного технічного університету "Харківський політехнічний інститут", забезпечує підготовку бакалаврів і магістрів за проектно-орієнтованою освітньою програмою за напрямом науки про дані "DataScience".

У складі науково-педагогічного колективу кафедри працюють: 3 доктора наук: 1 – технічних, 1 – фізико-математичних, 1 – педагогічних; 15 кандидатів наук: 10 – технічних, 4 – фізико-математичних, 1 – педагогічних; 3 співробітників мають звання професора, 9 – доцента.

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Фільтри

2016 - 20172

Налаштування

ORCID: search.filters.orcid.https://orcid.org/0000-0002-9015-4016Ключові слова: search.filters.subject.комплексний критерій

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  • Ескіз
    Документ
    Finding the probability distribution of states in the fuzzy markov systems
    (Technology center PC, 2017) Raskin, Lev; Sira, Oksana; Katkova, Tetiana
    A problem on finding the stationary distributions of probabilities of states for the Markov systems under conditions of uncertainty is solved. It is assumed that parameters of the analyzed Markov and semi-Markov systems (matrix of transition intensities, analytical description of distribution functions of the durations of being in states of the system before exiting, as well as a matrix of transition probabilities) are not clearly assigned. In order to describe the fuzziness, we employ the Gaussian membership functions, as well as functions of the type. The appropriate procedure of systems analysis is based on the developed technology for solving the systems of linear algebraic equations with fuzzy coefficients. In the problem on analysis of a semi-Markov system, the estimation of components of the stationary distribution of probabilities of states of the system is obtained by the minimization of a complex criterion. The criterion considers the measure of deviation of the desired distribution from the modal one, as well as the level of compactness of membership functions of the fuzzy result of solution. In this case, we apply the rule introduced for the calculation of expected value of fuzzy numbers. The criterion proposed is modified through the introduction of weight coefficients, which consider possible differences in the levels of requirements to different components of the criterion.
  • Ескіз
    Документ
    Method of solving fuzzy problems of mathematical programming
    (Technology center PC, 2016) Raskin, Lev; Sira, Oksana
    A brief analysis of traditional methods of solving fuzzy problems of mathematical programming was carried out. The shortcomings of the known approaches, limiting their application for the problems of real dimensionality, were revealed. The solution of the problem is achieved with the use of a two–stage procedure. At the first stage, a usual optimization problem is solved, which is caused by the original problem with the replacement of fuzzy parameters with their modal values. In this case, standard technologies of solving the problems of mathematical programming are used. At the second stage, a distinct solution, which satisfies two special requirements, is searched for. First, this solution must minimally deviate from the modal, obtained at the first stage. Second, membership function of fuzzy value of the optimized function, corresponding to the solution, must have a minimum level of uncertainty. In this connection, a complex criterion, which contains two appropriate components, is formed for solving the problem. A parameter of regularization, which assigns the value of the weight coefficient, determining the value of components, is introduced into the proposed complex criterion. This regulating multiplier provides acceptable level of the ratio between contradictory requirements, corresponding to the components of the criterion. The proposed approach for solving the problem of mathematical programming with not clearly defined parameters has the following benefits. Complex criterion has a distinct meaning and the corresponding computational procedure is simple. The implementation of its first stage is ensured by a traditional set of tools of determined optimization. The problem of the second stage when using standard membership functions, as a rule, comes down to the problem of quadratic programming. The account of theoretical material of the work is accompanied by examples.