This could be the concept you are looking for:

Cost curves.

https://link.springer.com/content/pdf/10.1007/s10994-006-8199-5.pdf

The concept is ROC curve but with cost associated for every type of cost.

For example: False negatives have a cost of 100. False positives have a cost of 5. Using cost-associated ROC curves will help you punishing much more FN than FP or viceversa.

This could be the concept you are looking for:

Cost curves.

The concept is ROC curve but with cost associated for every type of cost.

For example: False negatives have a cost of 100. False positives have a cost of 5. Using cost-associated ROC curves will help you punishing much more FN than FP or viceversa.