In this paper, we firstly introduce bijective soft matrix theory and research its operations, properties and algebraic structures in detail. Also, we present a bijective soft decision system based on the bijective soft matrix theory. Moreover, we construct a multi-bijective linguistic soft decision system by employing the matrices corresponding to the bijective soft sets generated from the linguistic variable parameters. Finally, the system's decision algorithm and its application for a decision making problem are given. By using the algorithm, we determine both the linguistic variables according to the parameters and the parameters affecting the optimal choice according to the highest linguistic decision value.