This paper considers multiobjective optimization under uncertainty (MOOUC) for the selection of optimal cutting conditions in advanced abrasive machining (AAM) processes. Processes considered are water jet machining (WJM), abrasive water jet machining (AWJM), and ultrasonic machining (USM). Decisions regarding the cutting conditions can involve optimization for multiple competing goals, such as surface finish, machining time, and power consumption. In practice, there is also an issue of variations in the ability to attain the performance goals. This can be due to limitations in machine accuracy or variations in material properties of the workpiece and/or abrasive particles. The approach adopted in this work relies on a strength Pareto evolutionary algorithm (SPEA2) framework, with specially tailored dominance operators to account for probabilistic aspects in the considered multiobjective problem. Deterministic benchmark problems in the literature for the considered machining processes are extended to include performance uncertainty and then used in testing the performance of the proposed approach. Results of the study show that accounting for process variations through a simple penalty term may be detrimental for the multiobjective optimization. On the other hand, a proposed fuzzy-tournament dominance operator appears to produce favorable results.