Abstract To study the problem of multiple attribute decision making in which the decision making information values are triangular fuzzy number, a new group decision making method is proposed. Then the calculation steps to solve it are given. As the key step, a new operator called fuzzy induced ordered weighted harmonic mean (FIOWHM) operator is proposed and a method based on the fuzzy weighted harmonic mean (FWHM) operator and FIOWHM operators for fuzzy MAGDM is presented. The priority based on possibility degree for the fuzzy multiple attribute decision making problem is proposed. At last, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.