How to get an absolute value of Around?

Question

Around is a useful feature of Mathematica 12 to work with uncertain data.

x = Around[-1, {0.5, 1.5}]

$-1.0^{+1.5}_{-0.5}$

I'm curious how to get an absolute value of such uncertain data. When I use Abs directly I get an unexpected result:

Abs[x]

$1.0^{+1.5}_{-0.5}$

I have expected: $1.0^{+0.5}_{-1.0}$, because

Abs[x["Interval"]]

Interval[{0, 1.5}]

In total there are two issues:

1. Upper and lower uncertainties are not interchanged when taking Abs.

2. Crossing of zero is ignored.

Is this intended behaviour of Around or some sort of a bug?

How should I calculate absolute values of uncertain data points? For example, when I want to plot Abs of uncertain of data?

Update

Simple multiplication by a negative number gives incorrect result:

(-1)*x

$1.0^{+1.5}_{-0.5}$ (* Correct answer is $1.0^{+0.5}_{-1.5}$*)

Answer 1

I don't know if this would be acceptable as an answer, for the sake of expediency (assuming you just want a quick answer!), here is what you could write to keep this working for you:

abs[val_, lBound_, uBound_] := 
  Around[Abs[val], 
   If[val > 0, {lBound, uBound}, Reverse@{lBound, uBound}]];
abs[-1, 0.5, 1.5]

I hope this helps.