Алгоритм нечітких кількісних обчислень для оперативних розрахунків

Performing arithmetic computations during operational calculations is almost always associated with quantitative values that can only be estimated approximately. Examples include the distance to the front line (line of contact), the number of weapons and military equipment, the time required to execute a maneuver, and others. The uncertainty of quantitative values may arise from various sources, such as incomplete data, imprecise linguistic descriptions, or other factors. To perform arithmetic operations under such conditions, the user must have at least three tools for: defining the values of initial fuzzy quantities; calculating the resulting fuzzy quantities (in most cases, four basic arithmetic operations – addition, subtraction, multiplication, and division – as well as ranking are sufficient); computing the characteristics of the resulting fuzzy quantities for decision-making. The aim of this study is to develop an algorithm for quantitative computations with fuzzy numbers that restricts the growth of the support of the result when performing multiple arithmetic operations. This paper proposes a new algorithm of fuzzy arithmetic (performing arithmetic operations with operands represented as fuzzy numerical values) for operational calculations. Unlike known algorithms, the proposed one effectively constrains the expansion of the result’s support in a sequence of multiple arithmetic operations, making it suitable for operational calculations under uncertainty. This improvement enhances the quality of data for decision-making in practice, which is particularly important when carrying out a large number of arithmetic operations in operational contexts. Although the algorithm has relatively high computational complexity, this does not hinder its implementation in software, considering the performance of modern computers.