Abstract
This paper introduces Asymmetric Interval Numbers (AINs), a novel type of interval numbers that combines the straightforward identification characteristic of classical interval numbers with the advanced capability for modeling uncertainty found in fuzzy sets, all while maintaining simplicity. AINs incorporate the expected value within the interval, providing a more accurate representation of the uncertainty of the data compared to the classical interval numbers. We define basic arithmetic operations for AINs, discuss their properties, and provide proofs. Additionally, we present theorems on symmetry and asymmetry for fundamental binary and unary operations, enhancing the mathematical framework for AINs. Several illustrative examples demonstrate the practical application of AINs. Although challenges remain, such as exploring performance with different distributions and reducing overestimation, AINs present a promising advancement in interval arithmetic. This study underscores the practical and theoretical implications of AINs, paving the way for further research and application in diverse scientific and industrial contexts.
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