We extend the decentralized signal detection problem to the case where the observations available at the sensors display measurement inaccuracy. The imprecise measurements at each sensor are modeled as fuzzy information systems. The fuzzy information system model consists of fuzzy partitions defined on the corresponding crisp (nonfuzzy) observation space. A Bayesian decision criterion is employed in the design of the signal detection schemes at the local sensors and the decision fusion center. Compression of the input fuzzy systems at the sensors into a fewer number of levels is studied. Both optimal and suboptimal methods are employed to partition the fuzzy observation space for signal detection applications.