Abstract: This paper transformed uncertain multi-attribute decision-making into the uncertain multi-attribute case retrieval question, and used the case reasoning method to gain the most similar case which is the approximate solution of the goal decision-making questions.The difference was reduced between the approximate solution and the solution of the goal decision-making question through case revision until completely consistent.This paper systematically propo sed a case retrieval algorithm(RA-UMDM) which is fit for the retrieval request of the uncertain multi-attribute question, and emphatically studied the fuzzy set based on the trapezoid and improved retrieval algorithm based on Eulerian-Lagrangian distance which would be used to solve in separately the case fuzzy concept attribute, the similarity of sector characteristic attribute and the case weight adjustment.This paper applied this method in the dentistry assistance diagnosis decision-making process and obtained a more accurate solution, and then tested the validity, accuracy and efficiency of RA-UMDM algorithm.It was demonstrated that RA-UMDM could satisfy the retrieval requirements of uncertain multi-attribute decision-making with high retrieval speed and quality.

Key words: multi-attribute decision-making, uncertain, case, retrieval algorithm, clustering