Organizing fingerings, i.e., choosing which fingers to press on which positions and strings, is a crucial step for playing the violin. As the violin fingering comprises several components, the mapping of a musical phrase to the corresponding fingering arrangement is not unique, and it requires comprehensive musical knowledge for organizing adequate fingerings. In this paper, we study the human-machine cooperative approach to the generation of violin fingering, aiming to build an intelligent system which can provide multiple generation paths and yield adaptable fingering arrangements. For this sake, we compile a new dataset with fingering annotations of multiple versions of performance, propose a deep neural network with conditions on the left-hand movement for fingering generation, and conduct an in-depth user study for detailed responses. Result shows that the proposed system can yield various fingering arrangements according to different performance requirements, though a single generation may not satisfy all the requirements at a time. This highlights the importance of multi-path and human-in-the-loop architecture for violin fingering generation.