© 2022 IEEE.Cooperative networks based on Non-Orthogonal Multiple Access (NOMA) is a promising radio access technology to cope with the challenging requirements of 5G and beyond systems. The power allocation in a cooperative NOMA system is a challenging task having a significant impact on the user perceived quality of service. In this paper, an adaptive power allocation technique is proposed using Fuzzy Logic (FL) for cooperative NOMA with imperfect successive interference cancellation (SIC). The FL system is trained to provide the power allocation coefficient by systematically varying signal-to-noise ratios (SNRs) at relays and users and randomly assigning all wireless channel coefficients. The power is allocated between the NOMA user pair within a resource block in such a way that the rate fairness is maximized and the system outage is minimized. The numerical results obtained by FL are close to the optimum outage probabilities and rate fairness results for all experiments when the number of relays and SNRs are varied. The results are promising since the computationally efficient FL can be successfully utilized at the run time for allocating power in a cooperative NOMA system.