The incredible impact of nanodecagonal fuzzy number and its arithmetic operations

Mathematical modeling under uncertainty requires robust fuzzy representations to handle imprecise data effectively. Traditional fuzzy numbers, such as triangular and trapezoidal, may be inadequate in cases of heightened uncertainty. To overcome these limitations, we introduce nanodecagonal fuzzy numbers (NDFNs), an advanced extension of higher-order fuzzy numbers, offering greater precision and adaptability. This paper formally defines NDFNs, investigates their structural properties, and establishes arithmetic operations, including addition, subtraction, and multiplication, supported by illustrative examples. Furthermore, the study explores the defuzzification process, which converts fuzzy values into crisp numerical outputs, enhancing their practical applicability. The proposed framework expands the utility of fuzzy numbers in complex decision-making and computational models, making them more suitable for handling real-world uncertainty.