Asymmetric interval numbers: A new approach to modeling uncertainty

Abstract

This paper introduces Asymmetric Interval Numbers $\left(AINs\right)$, 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.