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Due to a high propagation delay in Underwater Sensor Networks (UWSNs), i.e., Spatial-Temporal Uncertainty, traditional approaches for solving the max-min fairness issue in terrestrial MACs do not work well in UWSNs. In this work, we address the max-min fairness problem in (UWSNs). First, Time Expanded Conflict Graph (TiE-CG) and Time Expanded Clique (TiE-Clique) are proposed to represent the conflict and clique relationships under spatial-temporal uncertainty. We devise an algorithm and integer linear programming model to assign max-min fairness rates. The results show that our approach can achieve max-min fairness and have higher system throughput.