According to the characteristics of the decision factors of supporting schemes for deep foundation pit

such as information incompleteness and their gray correlation

using gray system theory

vector projection synthetically and fuzzy mathematic theory

a fuzzy gray relation projection method for the optimization of supporting schemes is established based on the gray relation projection method. Combined weights are used to interpret the impact of various factors more reasonable. A method for sensitivity analysis which bases on the distinguishing degree of the optimal plan is presented. Then the model is proved scientifically and effective by an example and easy to realize programmed. The algorithm which has the high sensitivity level offers more reliable basis for decision-making. So it has some generalization and application value