In this paper, a full-duplex (FD) cooperative uplink (UL) non-orthogonal multiple access (NOMA) network is studied, where a far user communicates with a base station via a direct link and user relaying. It is assumed that there exist randomly located M users in the vicinity wishing to share the same spectrum, one of which is selected and paired with far user by maxmin selection. The analytical derivations are performed for the outage probabilities of both users when three successive interference cancellation (SIC) schemes are adopted: channel state information (CSI)-based, quality of service (QoS)-based and hybrid SIC. The main issue in UL-NOMA networks is the inevitable error floor in the selected user's performance curves at high signal-to-noise ratio region. The hybrid SIC eliminates the error floor by adaptively changing the SIC decoding order and provides robustness to self-interference due to FD, in terms of selected user's outage performance, unlike the CSI-based and QoS-based SIC. It is shown that the selected user's performance can be further improved by power allocation besides the improved performance of far user by cooperation. The superiority of the hybrid SIC protocol for UL-FD-NOMA over reference half-duplex (HD) NOMA and OMA is demonstrated. Moreover, the results show that the performance of both users improves with increasing M. (C) 2022 Elsevier Inc. All rights reserved.