Before revision:  Based on the system decomposition theory , the indirect transactions and the corresponding indirect requirements matrix are introduced in the present article for the first time. This novel concept of the indirect transactions is also compared with some existing indirect effect formulations, and the theoretical advancement brought by the proposed methodology is discussed. It is shown theoretically and through illustrative examples that the proposed indirect transactions accurately describe and quantify the indirect interactions and relationships , unlike the current indirect effects formulations.
After revision:  Based on the system decomposition theory . It is demonstrated theoretically and through illustrative examples that the proposed indirect transactions accurately describe and quantify the indirect interactions and relationships , unlike the current indirect effects formulations.