title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ðµ ÑÑÐµÑÐ³Ð¾Ð»ÑÐ½ÑÑ ÑÐ¸ÑÐµÐ» Ð² Ð·Ð°Ð´Ð°ÑÐµ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ Ð¸Ð·Ð¾ÑÐ¾Ð¿Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Numerical inversion of triangular numbers in the problem of isotope data processing
Creators: name: ÐÑÐ·Ð¸Ð½, ÐÐ²Ð°Ð½
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑ
Ð½ÐµÑÐµÑÐºÐ¸Ðµ ÑÑÐµÑÐ³Ð¾Ð»ÑÐ½ÑÐµ ÑÐ¸ÑÐ»Ð°
Ð°Ð»ÑÑÐµÑÐ½Ð°ÑÐ¸Ð²Ð½Ð°Ñ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ° Ð½ÐµÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÐµÐ»
Ð¼ÐµÑÐ¾Ð´ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ Ð½ÐµÑÐµÑÐºÐ¸Ñ ÑÑÐµÑÐ³Ð¾Ð»ÑÐ½ÑÑ ÑÐ¸ÑÐµÐ»
Ð¸Ð·Ð¾ÑÐ¾Ð¿Ð½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ
Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð°Ñ Ð°ÑÐ¾Ð¼Ð½Ð°Ñ Ð¼Ð°ÑÑÐ°
uncertainty
fuzzy triangular numbers
alternative arithmetic of fuzzy numbers
method of inversion of fuzzy triangular numbers
isotope data
relative atomic mass

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description: The present paper introduces an approach to using alternative arithmetic of fuzzy triangular numbers for processing isotopic data. The general concepts and classification of isotopic distributions are considered, as well as an analysis of standard arithmetic defined by the Zadeh extension principle. The method of inverting fuzzy triangular numbers, constructed on alternative arithmetic, was studied and applied to solve problems related to isotopic data analysis. Triangular numbers were used to model uncertainty and fuzziness in data on the relative atomic mass of chemical elements in substances. Examples of inverting constructed triangular numbers in such a formulation for modeling uncertainty and fuzziness in data on the relative atomic mass of chemical elements are presented, which allows for the consideration of various possible values of atomic masses of elements in samples and increases the quality and accuracy. In conclusion, the prospects for further development of this approach in the field of isotopic data processing and other areas of science and technology where working with uncertainty and fuzziness in data during analysis is required were outlined.