  Inequality measures provide a valuable tool for the analysis, comparison, and
optimization based on system models. This work studies the relation between
attributes or features of an individual to understand how redundant, unique,
and synergetic interactions between attributes construct inequality. For this
purpose, we define a family of inequality measures (f-inequality) from
f-divergences. Special cases of this family are, among others, the Pietra index
and the Generalized Entropy index. We present a decomposition for any
f-inequality with intuitive set-theoretic behavior that enables studying the
dynamics between attributes. Moreover, we use the Atkinson index as an example
to demonstrate how the decomposition can be transformed to measures beyond
f-inequality. The presented decomposition provides practical insights for
system analyses and complements subgroup decompositions. Additionally, the
results present an interesting interpretation of Shapley values and demonstrate
the close relation between decomposing measures of inequality and information.
