Let R be a relation with attribute set U, and X, Y are subsets of U. X_g1(t1) -> Y_g2(t2) is a type-M functional dependency (MFD) relation if and only if for any two tuples u1 and u2 in R that u1[X] is g1(t1)-similar to u2[X], then u1[Y] is g2(t2)-similar to u2[Y], where g1 is in TD(X) (the set of tuple-distance functions defined on X) and g2 is in TD(Y) (the set of tuple-distance functions defined on Y), and t1 and t2 in the closed interval [0,1] are thresholds.