For the problem of multi-attribute decision making, in which the attribute values are the interval-valued trapezoidal
intuitionistic fuzzy numbers and the weights of attributes are intervals, a decision making method is proposed based on
fractional programming. Hamming and Euclidean distances for interval-valued trapezoidal intuitionistic fuzzy numbers are
defined. By using the TOPSIS(technique for order preference by similarity to an ideal solution), the models of non-linear
fractional programming for alternative’s relative closeness are built. Through the Charnes and Cooper transformations, these
non-linear models are transformed into linear programming models. The interval of alternative’s relative closeness is obtained
by solving these linear programming models, and the method of decision making is given. The numerical example analysis
shows the effectiveness of the method.