In this paper, we investigate the uplink transmission for user-centric cell-free massive multiple-input multiple-output (MIMO) systems. The largest-large-scale-fading-based access point (AP) selection method is adopted to achieve a user-centric operation. Under this user-centric framework, we propose a novel inter-cluster interference-based (IC-IB) pilot assignment scheme to alleviate pilot contamination. Considering the local characteristics of channel estimates and statistics, we propose a location-aided distributed uplink combining scheme based on a novel proposed metric representing inter-user interference to balance the relationship among the spectral efficiency (SE), user equipment (UE) fairness and complexity, in which the normalized local partial minimum mean-squared error (LP-MMSE) combining is adopted for some APs, while the normalized maximum ratio (MR) combining is adopted for the remaining APs. A new closed-form SE expression using the normalized MR combining is derived and a novel metric to indicate the UE fairness is also proposed. Moreover, the max-min fairness (MMF) power control algorithm is utilized to further ensure uniformly good service to the UEs. Simulation results demonstrate that the channel estimation accuracy of our proposed IC-IB pilot assignment scheme outperforms that of the conventional pilot assignment schemes. Furthermore, although the proposed location-aided uplink combining scheme is not always the best in terms of the per-UE SE, it can provide the more fairness among UEs and can achieve a good trade-off between the average SE and computational complexity.