Fuzzy multiple attribute decision making (FMADM) is an efficient way to solve complex systems, and has wide, practical application. This paper studies the FMADM of the trapezoidal fuzzy number. In order to achieve desirable decision making, the similarity measures between two trapezoidal fuzzy numbers is defined, which is based on a new method for ranking fuzzy numbers. A new algorithm is proposed to remove surplus attributes. This algorithm is based on rough sets and the technique for order of preference by similarity to ideal solution (TOPSIS) method; Finally, an example is examined to demonstrate the model's use in practical problems.