## CASPIAN JOURNAL

### MANAGEMENT AND HIGH TECHNOLOGIES

##### MATHEMATICAL MODEL FOR ESTIMATING THE QUALITY OF ELECTRONIC LIBRARY: SYNTHESIS OF THE NUMBER OF GRADATIONS OF SPACE STATES

Read | Kryukova Elena S., Parashchuk Igor B. MATHEMATICAL MODEL FOR ESTIMATING THE QUALITY OF ELECTRONIC LIBRARY: SYNTHESIS OF THE NUMBER OF GRADATIONS OF SPACE STATES // Caspian journal : management and high technologies. — 2020. — №1. — pp. 121-131. |

**Kryukova Elena S.** - Military Academy of Communications named after Marshal of the Soviet Union S.M. Budyonny, e.kkrukovaa69@yandex.ru

**Parashchuk Igor B.** - Military Academy of Communications named after Marshal of the Soviet Union S.M. Budyonny, shchuk@rambler.ru

The place of electronic libraries in the information and educational space and the education system of Russia is shown. The features of a mathematical model for evaluating the quality of an electronic library are characterized. The stages of the algorithm for finding the minimum allowable values of the increments (number of gradations) of state variables describing the dynamics of changing the values of the quality indicators of the electronic library, as well as the search for optimal time intervals for their discretization, are considered. An algorithm is proposed for determining the optimal number of gradations of state spaces for constructing a model of an electronic library. The algorithm takes into account the requirements for accuracy (deviation value) of the quality assessment criterion, for the stability of the main operational and technical indicators of the electronic library with respect to disturbing influences, as well as current user requirements for the mathematical complexity of assessing the quality of an object of this class. Analytical expressions are formulated to find the permissible error in estimating the value of the l - th quality indicator, sensitivity coefficient and the sampling time interval of the components of the vector quality indicator of the electronic library. The proposed approaches make it possible to formulate a reliable (adequate to control problems) mathematical model in the interests of assessing the quality of the electronic library, open up new possibilities for modeling the state of libraries and predict their quality, deepen our understanding of the mathematical nature of the process of changing states of complex controlled information technology systems and processes.

**Key words**: электронная библиотека, пространство состояний, показатель качества, оценивание, математическая модель, процесс смены состояний, марковская цепь, уравнение состояния, уравнение наблюдения, минимальное число градаций, переменные состояния, погрешность, вре