<p>The aim of this paper is provide an alternative way of deriving the weights of the van IJzeren additive decomposition of Fisher (price or quantity) indices, which is based on an aggregation rule rather than the axiomatic approach. In particular, it is showed that the van IJzeren additive decomposition weights can be obtained by relying on the denominator rule and the exact relation between the weights of the arithmetic and the geometric aggregations that result in the same aggregate value. In addition, we propose a new harmonic decomposition of Fisher (price or quantity) indices, which is reflexive and satisfactory, by using the numerator rule and the exact relation between the weights of the harmonic and the geometric aggregation that result in the same aggregate value that allows us to express the Fisher index as (the inverse of) a share-weighting harmonic aggregate of price or quantity relatives.</p>