Name for multiset with fractional amounts?
I don't know a standard name for this, but what you've described is representable as a function into $\mathbb{R}$.

For your example, if $X$ is the set of your things then you can represent your 'fractional multiset' as a a function $f : X \to \mathbb{R}$ such that

$$
f(x) = 
\begin{cases}
1 &amp; x = \text{carpenter}, \text{sawyer} \\
0.5 &amp; x = \text{woodcutter} \\
0.25 &amp; x = \text{forester} \\
0 &amp; \text{otherwise}
\end{cases}.
$$

If you're looking for a way to implement this in a programming language, if you need to store only finitely many things then you could use a map/dictionary data structure. For example in java you could use some implementation of Map&lt;X, Float&gt;

As for what to call this, "fractional multiset" sounds fine as long as you explain it in whatever context you're using. Alternately you could just refer to it as a "size/measurement function".