Hend Dawood
Yasser Dawood
2019-07-01
<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>
https://doi.org/10.5281/zenodo.3234186
oai:zenodo.org:3234186
eng
Zenodo
https://doi.org/10.5281/zenodo.3234184
https://doi.org/10.5281/zenodo.2656089
https://doi.org/10.5281/zenodo.2702404
https://doi.org/10.4018/978-1-4666-4991-0.ch001
https://zenodo.org/communities/mathscicu
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.3234185
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 01(03), 37-54, (2019-07-01)
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
Parametric Intervals: More Reliable or Foundationally Problematic?
info:eu-repo/semantics/article