Radio interference should be taken into account to assign time slots to links in time division multiple access (TDMA)-based wireless mesh networks. In many graph theorybased time slot assignment algorithms, the protocol interference model is widely used to obtain radio interference information, although this model is considered to be inaccurate when compared with actual radio interference. On the other hand, the signal-to-interference-plus-noise- ratio model (SINR model) is a well-known and accurate model of radio interference. However, the SINR model requires time slot information to obtain radio interference relationship, and thus it is difficult to apply the SINR model to graph theory-based time slot assignment algorithms. In this paper, we extend the protocol interference model to represent radio interference more accurately for wireless mesh networks. To do this, we adjust the interference ratio parameter of the protocol interference model by considering SINR. We propose three methods for adjusting this parameter. Through simulation, it is shown that higher accuracy of the protocol interference model can be achieved by adjusting the interference ratio parameter for each node.