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We consider the problem of decision fusion in mobile wireless sensor networks where the channels between the sensors and the fusion center are time-varying. We assume that the sensors make independent local decisions on the M hypotheses under test and report these decisions to the fusion center using differential phase-shift keying (DPSK), so as to avoid the channel estimation overhead entailed by coherent decision fusion. For this setup we derive the optimal and three low-complexity, suboptimal fusion rules which do not require knowledge of the instantaneous fading gains. The suboptimal fusion rules are obtained by applying certain approximations to the optimal fusion rule and are referred to as Chair-Varshney (CV), ideal local sensors (ILS), and max-log fusion rules. Since all proposed fusion rules exploit an observation window of at least two symbol intervals, we refer to them collectively as multiple-symbol differential (MSD) fusion rules. For binary hypothesis testing, we derive performance bounds for the optimal fusion rule and exact or approximate analytical expressions for the probabilities of false alarm and detection for all three suboptimal fusion rules. Simulation and analytical results show that whereas the CV and ILS fusion rules approach the performance of the optimal fusion rule for high and low channel signal-to-noise ratios (SNRs), respectively, the max-log fusion rule performs close-to-optimal for the entire range of SNRs. Furthermore, in fast fading channels significant performance gains can be achieved for the considered MSD fusion rules by increasing the observation window to more than two symbol intervals.