МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ЗАДАЧИ ОПРЕДЕЛЕНИЯ НАБОРА КОНТРОЛЬНЫХ МЕРОПРИЯТИЙ С ПОМОЩЬЮ НЕЧЕТКОГО МЕТОДА АНАЛИЗА ИЕРАРХИЙ И МЕТОДА, ОСНОВАННОГО НА ИЗМЕРЕНИИ ЛАТЕНТНЫХ ПЕРЕМЕННЫХ
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Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
Online media
issn 2310-6018

MATHEMATICAL MODELING OF THE TASK OF DETERMINING A SET OF CONTROL EVENTS USING A FUZZY METHOD OF ANALYSIS OF HIERARCHIES AND A METHOD BASED ON MEASURING LATENT VARIABLES

Krasova N.E.,  Aleinikova N.A. 

UDC 519.876.2
DOI: 10.26102/2310-6018/2019.26.3.024

  • Abstract
  • List of references
  • About authors

The article discusses the mathematical modeling of the problem of multi-criteria selection of control measures for the ongoing monitoring of performance using two methods: a method of fuzzy analysis of hierarchies and a method based on measuring latent variables (the Rush method). Both methods are expert methods. The advantage of using a fuzzy hierarchy analysis method is to describe the relative attribute values using fuzzy numbers instead of exact ones. Due to this, the expert gets the opportunity not only to assess the degree of preference of one object over another, but also to express his doubts, experience, intuition in this assessment. The main disadvantage of this approach is the complexity and complexity of the calculations. The advantages of the Rush method are in the simplicity of calculations, in the transition from the subjective assessments of experts to the objective ones, which possess the property of linearity. Within the framework of the constructed hierarchical model aimed at increasing the efficiency of the learning process, weights of different types of control measures are determined by these methods. In the future, the weights obtained can be used as parameters in the models for the formation of a set of control measures based on minimizing the difficulty of their implementation and maximizing their usefulness.

1. Saaty T. Decision Making. Hierarchy analysis method. - M .: Radio and communications, 1993. –278 p.

2. Chang D.Y. Applications of the extent analysis method on fuzzy AHP / D.Y. Сhang // European Journal of Operational Research, V. 9, № 3, 1996. –P. 649- 655.

3. Mukhametzyanov I.Z. Fuzzy inference and fuzzy analysis of hierarchies in decision support systems: an application to assess the reliability of technical systems // Cybernetics and Programming, № 2, 2017. - P.59-77.

4. Vorontsov Ya.A. Parameterized comparison methods for fuzzy triangular and trapezoidal numbers / Ya.A. Vorontsov, M.G. Matveev // Vestnik VSU, series: System Analysis and Information Technologies, № 2, 2014.– P. 90-97.

5. Barkalov S.A. Application of the method of least squares in the evaluation of latent variables by the method of Russia / S.A. Barkalov, S.I. Moiseev, E.V. Solovyov // Scientific Bulletin of the Voronezh GASU. Ser. "Construction management". - Voronezh, 2014. Issue number 1 (6). -WITH. 98-100.

6. Kireev Yu.V. Application of the Rush model for evaluating latent variables in expert estimation. // Science and Modernity, №35, 2015. –C. 139-143.

Krasova Natalia Evgenievna
Candidate of Physical and Mathematical Sciences, Associate Professor
Email: krasovanata@mail.ru

Zhukovsky-Gagarin Air Force Academy

Voronezh, Russian Federation

Aleinikova Natalia Aleksandrovna
Candidate of Economic Sciences, Associate Professor
Email: balbashovan@mail.ru

Zhukovsky-Gagarin Air Force Academy

Voronezh, Russian Federation

Keywords: expert estimation methods, pairwise comparison matrix, fuzzy analysis of hierarchies, latent variables, rush method.

For citation: Krasova N.E., Aleinikova N.A. MATHEMATICAL MODELING OF THE TASK OF DETERMINING A SET OF CONTROL EVENTS USING A FUZZY METHOD OF ANALYSIS OF HIERARCHIES AND A METHOD BASED ON MEASURING LATENT VARIABLES. Modeling, Optimization and Information Technology. 2019;7(3). URL: https://moit.vivt.ru/wp-content/uploads/2019/09/KrasovaAleynikova_3_19_1.pdf DOI: 10.26102/2310-6018/2019.26.3.024 (In Russ).

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Published 30.09.2019