A general decomposition approach for multi-criteria decision trees

► We propose a decomposition-based recursive approach for multi-criteria decision trees. ► We state and prove a theorem of decomposition with four sufficient conditions. ► We characterize seven MCDA methods from different schools of thought. ► Results show that TOPSIS, ELECTRE III and PROMETHEE II do not fulfill the conditions. ► Impacts of independency, incomparableness, rank reversal, and thresholds are discussed.