Individual fairness is a fairness principle requiring that similar individuals be treated similarly by an AI or machine learning system. It depends on defining a meaningful similarity measure for the relevant context and can complement, but differ from, group fairness metrics.
A fairness metric that checks whether similar individuals are classified similarly. For example, Brobdingnagian Academy might want to satisfy individual fairness by ensuring that two students with identical grades and standardized test scores are equally likely to gain admission. Note that individual fairness relies entirely on how you define "similarity" (in this case, grades and test scores), and you can run the risk of introducing new fairness problems if your similarity metric misses important information (such as the rigor of a student's curriculum). See "Fairness Through Awareness" for a more detailed discussion of individual fairness.