In this paper, the notion of a projected context is proposed to explore a novel algorithm of computing triadic concepts of a triadic context, and a triadic decision context is defined by combining triadic contexts. Then a rule acquisition method is presented for triadic decision contexts. It can be considered as an information fusion technology for decision-making analysis of multi-source data if the data under each condition is viewed as a single-source data. Moreover, a knowledge reduction framework is established to simplify knowledge discovery. Finally, discernibility matrix and Boolean function are constructed to compute all reducts, which is beneficial to the acquisition of compact rules from a triadic decision context.