Abstract: To help determine the fuzzy membership degree and weight of fuzzy mathematics in  slope stability evaluation, we propose set-valued statistics for the degree of membership through fuzzy statistics of rough quotient set. Based on the range difference of factors affecting side slope stability obtained by neural network orthogonal analysis, we construct the judgment matrix through AHP (Analytic Hierarchy Process) to compute the weight, and introduce the fuzzy integral  theory which is more suitable for measurement and decision. Through the evaluation of slope samples and examples, we conclude that the accuracy of fuzzy integral evaluation results is in a positive correlation with the number of factors, and the results are consistent with those of other theoretical methods and engineering practices. This method is feasible, reliable, and the calculation process is more convenient.

Key words: side slope stability, rough quotient set, fuzzy statistics, AHP, fuzzy integral evaluation