We investigate the problem of dynamic sensor activation for decentralized decision making in partially observed discrete-event systems, where the system is monitored by a set of agents. The sensors of each agent can be turned on/off online dynamically according to a sensor activation policy. We define a general decentralized decision-making problem called the decentralized state disambiguation problem, which covers the decentralized control problem, the decentralized fault diagnosis problem, and the decentralized fault prognosis problem. The goal is to find a language-based minimal sensor activation policy for each agent such that the agents can always make a correct global decision as a team. A novel approach to solve this problem is proposed. We adopt a person-by-person approach to decompose this decentralized minimization problem into two centralized constrained minimization problems. Each centralized constrained minimization problem is then reduced to a fully centralized sensor activation problem that is solved effectively in the literature. The solution obtained is provably language-based minimal with respect to the system language.