In open and dynamic Internet environment,multi-periods quality of service (QoS),multiple decision-makers based on heterogeneous QoS models and uncertainty weights make optimal Web service selection hard.To solve the difficulties above,dynamic Web service selection group decision-making based on heterogeneous QoS models (DWSSGD_HQM) is proposed.Drawing on and extending technique for order preference by similarity to ideal solution (TOPSIS),DWSSGD_HQM supports multiple decision-makers based on heterogeneous QoS models expressed in real numbers,interval numbers,triangular fuzzy numbers and intuitionistic fuzzy numbers respectively,and takes multi-periods QoS and weights of user and group into account.Six steps are detailed.They are converting heterogeneous QoS models into ones expressed in interval numbers,calculating weighted normalized decision-matrix,determining the group positive-ideal and negative-ideal solutions,calculating the close-degrees of candidates,aggregating close-degrees of multi-periods for each decision-maker,and ranking the alternatives.Finally,experiments are conducted by using actual QoS data to evaluate the effectiveness of the proposed approach.