The widespread use of Artificial Intelligence (AI) based decision-making systems has raised a lot of concerns regarding potential discrimination, particularly in domains with high societal impact. Most existing fairness research focused on tackling bias relies heavily on the presence of class labels, an assumption that often mismatches real-world scenarios, which ignores the ubiquity of censored data. Further, existing works regard group fairness and individual fairness as two disparate goals, overlooking their inherent interconnection, i.e., addressing one can degrade the other. This paper proposes a novel unified method that aims to mitigate group unfairness under censorship while curbing the amplification of individual unfairness when enforcing group fairness constraints. Specifically, our introduced ranking algorithm optimizes individual fairness within the bounds of group fairness, uniquely accounting for censored information. Evaluation across four benchmark tasks confirms the effectiveness of our method in quantifying and mitigating both fairness dimensions in the face of censored data.