The Free On-line Dictionary of Computing (30 December 2018):

partial equivalence relation (PER) A relation R on a set S where R is symmetric (x R y => y R x) and transitive (x R y R z => x R z) and where there may exist elements in S for which the relation is not defined. A PER is an equivalence relation on the subset for which it is defined, i.e. it is also reflexive (x R x).