In this paper, we propose F2-Bubbles, a set overlay visualization technique that addresses overlapping artifacts and supports interactive editing with intelligent suggestions. The core of our method is a new, efficient set overlay construction algorithm that approximates the optimal set overlay by considering set elements and their non-set neighbors. Thanks to the efficiency of the algorithm, interactive editing is achieved, and with intelligent suggestions, users can easily and flexibly edit visualizations through direct manipulations with local adaptations. A quantitative comparison with state-of-the-art set visualization techniques and case studies demonstrate the effectiveness of our method and suggests that F2-Bubbles is a helpful technique for set visualization.