Reevaluating Parametric Intervals: A Critical Examination of Their Foundations
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2019
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| author | Amira F. Khalil and Khaled M. Rashad |
| author_facet | Amira F. Khalil and Khaled M. Rashad |
| contents | <p>Interval arithmetic has been proved to be very subtle, reliable, and most fundamental in addressing uncertainty and imprecision. However, the theory of classical interval arithmetic and all its alternates suffer from algebraic anomalies, and all have difficulties with interval dependency. A theory of interval arithmetic that seems promising is the theory of parametric intervals. The theory of parametric intervals is presented in the literature with the zealous claim that it provides a radical solution to the long-standing dependency problem in the classical interval theory, along with the claim that parametric interval arithmetic, unlike Moore's classical interval arithmetic, has additive and multiplicative inverse elements, and satisfies the distributive law. So, does the theory of parametric intervals accomplish these very desirable objectives? Here it is argued that it does not.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19307788 |
| institution | Zenodo |
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| publishDate | 2019 |
| publisher | Zenodo |
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| spellingShingle | Reevaluating Parametric Intervals: A Critical Examination of Their Foundations Amira F. Khalil and Khaled M. Rashad Interval mathematics Classical interval arithmetic Parametric interval arithmetic Constrained interval arithmetic Overestimation-free interval arithmetic Interval dependency Functional dependence Dependency predicate Interval enclosures S-semiring Uncertainty Reliability <p>Interval arithmetic has been proved to be very subtle, reliable, and most fundamental in addressing uncertainty and imprecision. However, the theory of classical interval arithmetic and all its alternates suffer from algebraic anomalies, and all have difficulties with interval dependency. A theory of interval arithmetic that seems promising is the theory of parametric intervals. The theory of parametric intervals is presented in the literature with the zealous claim that it provides a radical solution to the long-standing dependency problem in the classical interval theory, along with the claim that parametric interval arithmetic, unlike Moore's classical interval arithmetic, has additive and multiplicative inverse elements, and satisfies the distributive law. So, does the theory of parametric intervals accomplish these very desirable objectives? Here it is argued that it does not.</p> |
| title | Reevaluating Parametric Intervals: A Critical Examination of Their Foundations |
| topic | Interval mathematics Classical interval arithmetic Parametric interval arithmetic Constrained interval arithmetic Overestimation-free interval arithmetic Interval dependency Functional dependence Dependency predicate Interval enclosures S-semiring Uncertainty Reliability |
| url | https://doi.org/10.5281/zenodo.19307788 |