The ranking of features according to a feature selection criteria is examined. The concept ofepsilon-equivalence is introduced to measure the extent to which a ranking deviates from the ranking included by the probability of error role. The relationship between theepsilon-equivalence of a given role and the bounds on the probability of error derived from this rule is demonstrated. Illustrations of theepsilon-equivalence concept are presented for Shannon's equivocation rule, the quadratic equivocation rule, and the Bhattacharyya rule. A numerical example concludes the presentation.