Classification accuracy of a Random Multi-label Classifier
In the context of a multi-label classifier (that is, having potentially more than one label per data point) we can have a prediction which is either fully correct, partially correct or fully incorrect. To account for this, the following accuracy metric has been proposed:
$$\text{Accuracy} = \frac{1}{n}\sum_{i=1}^n\frac{|T_i \cap P_i|}{|T_i\cup P_i|},$$
where $n$ is the sample size, $|\cdot|$ denotes the number of elements of a set, $T_i$ is the set of true labels and $P_i$ is the set of predicted labels for an item of the sample. 

For instance, let's say the $i$-th item has actual labels $A, B, C$ and $D$ (that is $T_i = \{A, B, C, D\}$, but your classifier predicts labels $B, D$ and $E$ (that is $P_i =\{B, D, E\}$), then you'd get
$$\frac{|T_i\cap P_i|}{|T_i\cup P_i|}=\frac{|\{B,D\}|}{|\{A,B,C,D,E\}|}=\frac{2}{5}.$$
To get the accuracy for the entire training set, you calculate this for each instance $i=1,\dots, n$ and you average it out.

You can also have a look at the evaluation metrics section of the article in Wikipedia about multi-label classifiers: https://en.wikipedia.org/wiki/Multi-label_classification#Statistics_and_evaluation_metrics