Modeling Uncertainty in Engineering Problems Using Asymmetric Interval Numbers (AINs)

Szymon Śniegowski; Adrianna Świder; Andrii Shekhovtsov; Wojciech Sałabun

doi:10.31181/smeor31202651

Authors

Szymon Śniegowski National Institute of Telecommunications, Warsaw, Poland Author https://orcid.org/0009-0005-7381-7323
Adrianna Świder West Pomeranian University of Technology in Szczecin, Szczecin, Poland Author https://orcid.org/0009-0009-3544-457X
Andrii Shekhovtsov National Institute of Telecommunications, Warsaw, Poland Author https://orcid.org/0000-0002-0834-2019
Wojciech Sałabun National Institute of Telecommunications, Warsaw, Poland Author https://orcid.org/0000-0001-7076-2519

DOI:

https://doi.org/10.31181/smeor31202651

Keywords:

Asymmetric Interval Numbers, AINs, Uncertainty Modeling, Engineering Analysis

Abstract

Engineering systems are increasingly complex and subject to multiple sources of uncertainty arising from geometric tolerances, material variability, and operating conditions, which significantly affect performance and reliability, making accurate modeling of uncertainty essential in modern engineering analysis. Classical interval analysis is a well-established approach for representing uncertainty; however, traditional interval numbers (CINs) assume a symmetric and uniform distribution around the central value, whereas in practice, uncertainties are often asymmetric due to uneven measurement errors, technological deviations, or differing consequences of overestimation and underestimation. As a result, symmetric intervals may distort risk assessment and reduce the accuracy of results. This study introduces Asymmetric Interval Numbers (AINs), a generalization of classical interval numbers that allows independent modeling of uncertainty in the positive and negative directions. AINs provide a more realistic and flexible framework for representing asymmetric data distributions while retaining the simplicity of interval analysis. To demonstrate their applicability, three case studies involving different classes of engineering problems were conducted, and the results show that AINs improve the realism, stability, and interpretability of uncertainty modeling compared with classical interval approaches, confirming their potential as an effective tool for engineering analysis.

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References

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