In 2-dimensional topologically ordered system with anyon excitations, we write the fusion of a anyon $a$ with another anyon $b$ outputting several possible outcomes, say anyons $c$. And there is a mysterious integer weight in the front of $c$, called the fusion rule or the fusion multiplicity

$N_{ab}^c$: $$a \times b = \sum_c N_{ab}^c c$$

- question 1: What are the physical meanings or physical observables for $N_{ab}^c$?

- question 2: does $N_{ab}^c$ say anything about the probability of having the anyon $c$ by fusing $a$ and $b$? Say, if $a \times b = N_{ab}^{c_1} c_1+ N_{ab}^{c_2} c_2$, then do $N_{ab}^{c_1}$ and $N_{ab}^{c_2}$ represent the probability weight of having a output anyon $c_1$ or $c_2$? Please try to answer this question from a experimental quantum physicist's perspective. Make the answer down to the earth. Thanks. :-)