A necessary and sufficient condition for decentralized control of discrete event systems via prioritized composition with exclusion (PCX) is provided. PCX was extended from prioritized synchronous composition (PSC) in order to model various Boolean modes of decision fusion by allowing the exclusivity of participation in system interactions . A notion of PCX-coobservability is introduced that captures the nature of PCX-based decision fusion, and a testing algorithm with polynomial complexity in the states of plant and specification is presented. The result is extended for multiple supervisors with multiple exclusivity sets based on an extended PCX definition.