Abstract
Different definitions of the entropy concept are analyzed. The concept of Shannon entropy for random variables is extended to uncertain variables that do not have a probability measure. The entropy concept is introduced for hyper-random and interval variables. We investigate different ways that uncertainty can arise. It is found that uncertainty may arise as a result of a certain type of nonlinear transformation and in the process of averaging determinate variables in the absence of convergence. We explain why the interval, multi-interval, and hyper-random models can adequately depict reality, while the random models are mathematical abstractions.
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Notes
- 1.
Exceptions are perhaps the cosmological constants, such as the speed of light and a small number of other physical constants that are accepted as unchanging by convention.
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Gorban, I.I. (2017). The Problem of Uncertainty. In: The Statistical Stability Phenomenon. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-43585-5_21
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DOI: https://doi.org/10.1007/978-3-319-43585-5_21
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