With the increasing complexity of multiple target tracking scenes, a single sensor may not be able to effectively monitor a large number of targets. Therefore, it is imperative to extend the single-sensor technique to Multi-Sensor Multi-Target Tracking (MSMTT) for enhanced functionality. Typical MSMTT methods presume complete randomness of all uncertain components, and therefore effective solutions such as the random finite set filter and covariance intersection method have been derived to conduct the MSMTT task. However, the presence of epistemic uncertainty, arising from incomplete information, is often disregarded within the context of MSMTT. This paper develops an innovative possibility Labeled Multi-Bernoulli (LMB) Filter based on the labeled Uncertain Finite Set (UFS) theory. The LMB filter inherits the high robustness of the possibility generalized labeled multi-Bernoulli filter with simplified computational complexity. The fusion of LMB UFSs is derived and adapted to develop a robust MSMTT scheme. Simulation results corroborate the superior performance exhibited by the proposed approach in comparison to typical probabilistic methods.