Trapezoidal function.

Gully erosion is one of the most severe forms of land degradation and poses a serious threat to regional food security, biodiversity, and human survival. However, there are few methods for the quantitative evaluation of gully activity, and the relationships between gully activity and influencing factors require further in-depth study. This study takes the Sunshui River Basin, as a case study. Based on field investigation, unmanned aerial vehicle (UAV) photography and remote sensing images, 71 typical gullies were identified. The vegetation coverage (VC), slope and main-branch gully ratio (MBGR) were used as evaluation indicators, and the gully activity was calculated using the fuzzy mathematics membership degree and then evaluated quantitatively. The factors influencing different active gullies were also analyzed. The results showed that (1) the fuzzy comprehensive evaluation method can be used to identify gully activity. Different levels of gully activity were defined based on the gully activity index. The active indices of stable gullies ranged from 0–0.25, those of semiactive gullies ranged from 0.25–0.75, and those of active gullies ranged from 0.75–1. (2) The activity indices of the 71 gullies ranged from 0.054 to 0.999, with an average value of 0.656. There are 31 active gullies, and 31 semiactive gullies. A total of 87.32% of the gullies in the study area were in the early or middle stage of gully development. Gully erosion was intense, which is consistent with the serious reality of soil erosion. (3) Gully activity was affected by multiple factors. It was significantly positively correlated with topographic relief (TR) (r = 0.64, PPPP