In the context of security engineering, it trust an equivalence relation?

This is the definition of an equivalence relation according to Wikipedia:

In mathematics, an equivalence relation is the relation that holds between two elements if and only if they are members of the same cell within a set that has been partitioned into cells such that every element of the set is a member of one and only one cell of the partition. The intersection of any two different cells is empty; the union of all the cells equals the original set. These cells are formally called equivalence classes.

My question is: In the context of security engineering, it trust an equivalence relation?