V.I. Levin


Context. In this paper we propose the dedetermination as the new method designed to solving a problem of calculation of deterministic
functions with the so-called singular points where the function does not take a certain value.
Objective. The approach is developed that allows for division by zero and thus exclude singular points of functions.

Method. The method proposed in this article is to move from the problematic (from point of view of calculating) determined function to the corresponding not determined (interval) function by replacing determined function parameters by corresponding interval parameters.
Due to this change values of the function at the singular points will be well-defined interval and values.
Results. The latter allows you to solve the problem of calculating the function. For the simplified by cutting out interval function the
effective formulas are derived based on main provisions of interval mathematics and make it easy to calculate value of this function. The
proposed in the article approach to the problem of calculating functions with singular points is important for all those classes of systems in
which the problem really exists. It is about the systems which functions have any number of specific points. Such systems are found mostly in
telemetry, reliability theory and practice, humanitarian and others areas. The features of these areas is that they do not always apply the
classical methods of deterministic mathematics. This leads us to search for new approaches to solving problems that arise here.
Conclusions. The solution to this problem is achieved by legalization division by zero by intervalization of calculations. It uses the
principle of cutting out a neighborhood of zero in the interval being the denominator of the fraction representing studied function.



interval; interval function; interval calculation; dedetermination; division by zero.


Гнеденко Б. В. Курс теории вероятностей / Б. В. Гнеденко. – М. : Наука, 2004. – 350 с. 2. Заде Л. А. Понятие лингвистической переменной и его применение к принятию приближенных решений / Л. А. Заде. – М. : Мир, 1976. – 165 с. 3. Алефельд Г. Введение в интервальные вычисления / Г. Алефельд, Ю. Херцбергер. – М. : Мир, 1987. – 360 с. 4. Горбань И. И. Феномен статистической устойчивости / И. И. Горбань. – К. : Наукова думка, 2014. – 370 с. 5. Wiener N. Extrapolation, Interpolation and Smoothing of Stationary Time Series / N. Wiener. – New-York: Technology Press and Wiley, 1949. – 180 p. 6. Колмогоров А. Н. Интерполирование и экстраполирование стационарных случайных последовательностей / А. Н. Колмогоров // Известия АН СССР. Серия : математика. – 1941. – № 5. – С. 3–14. 7. Канторович Л. В. О некоторых новых подходах к вычислительным методам и обработке наблюдений / Л. В. Канторович // Сибирский математический журнал. – 1962. – Т. 3, № 5. – С. 3–14. 8. Налимов В. В. Теория эксперимента / В. В. Налимов, Н. А. Чернова. – М. : Наука, 1971. – 320 с. 9. Нариньяни А. С. Недоопределенность в системе представления и обработки знаний / А. С. Нариньяни // Известия АН СССР. Техническая кибернетика. – 1986. – № 5. – С. 3–28.

GOST Style Citations

Copyright (c) 2017 V.I. Levin

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Address of the journal editorial office:
Editorial office of the journal «Radio Electronics, Computer Science, Control»,
National University "Zaporizhzhia Polytechnic", 
Zhukovskogo street, 64, Zaporizhzhia, 69063, Ukraine. 
Telephone: +38-061-769-82-96 – the Editing and Publishing Department.

The reference to the journal is obligatory in the cases of complete or partial use of its materials.