Decision-making processes in complex systems generally require the mechanisms to make the tradeoff among contradicting design criteria. When multiple objectives are involved in decision making or machine learning, a crucial step is to determine the weights of individual objectives to the system-level performance. Determining the weights of multiobjectives is an evaluation process, and it has been often treated as an optimization problem. However, our preliminary investigation has shown that existing methodologies in dealing with the weights of multiobjectives have some obvious limitations in the sense that the determination of weights is tackled as a single optimization problem, a result based on such an optimization is incomprehensive, and it can even be unreliable when the information about multiple objectives is incomplete such as an incompleteness caused by poor data. The constraints of weights are also discussed. Variable weights are natural in decision-making processes. Therefore, we are motivated to develop a systematic methodology in determining variable weights of multiobjectives. The roles of weights in an original multiobjective decision-making or machine-learning problem are analyzed, and the weights are determined with the aid of a modular neural network. The inconsistency issue of weights is particularly discussed.