Making decisions in a dynamic environment is complicated and indefinite because of various unpredictable factors and large volumes of information. It has become a key issue for modern organizations to have efficient systems and tools to support rational decision-making in problem-solving processes, particularly, for problems with a lack of predefined structure. This paper provides a novel agent-based framework for Decision Support Systems (DSS) based on the analysis of the major problems in existing DSS. The proposed multi-agent-based framework, namely the Agent-Matrices framework, provides an open, efficient and flexible architecture for DSSs. The Agent-Matrices framework overcomes the compatibility and connectivity problems in most traditional DSS applications. This framework utilises Matrices to allow agents to acquire information, self-upgrade, perform tasks, travel to other Matrices, and be reused. This paper primarily introduces the methods used for coordinating the Matrices and agents to solve a complex problem.