For the permutation importance a scaled version, the z-score, is available or even default in many implementations of random forests. The term “scaled” here is somewhat misleading, however, for two reasons: Firstly, the variable importance does not depend on the scaling or variance of the predictor variables in the first place (in fact, the whole method is invariant against the scaling of numeric variables). Therefore it is not necessary to account for the scaling of predictors in the variable importance.
