That only, at best, gives you the maximum and minimum values, with no knowledge of the actual distribution.
EDIT: Missed the specific request for interval arithmetic part for representation of numbers. Thought that was a proposal for the error propagation (which requires actual distributions and not simple min and max intervals).
Also, frink does not support accurate interval arithmetic for all operations, and reverts to numerically accurate bounds instead (https://frinklang.org/#IntervalArithmeticStatus). I don't know if Mathematica is any better for those.
https://frinklang.org/#IntervalArithmetic