Compatibility modification is a rule-based inference strategy that uses the similarity of the input with the antecedent of a rule to modify the consequent. Existing compatibility modification inference techniques have employed a set theoretic assessment of compatibility. In this paper, a distance-based compatibility measure is derived from a generalization of the dissemblance index for fuzzy sets. This measure is then used to develop an inference technique based on geometric compatibility. This geometric approach is compared with two other distance-based inference techniques: linear rule interpolation and bound dependent linear revision.