An important feature of the wireless network scenario is that there are multi-radio access technologies in the same area, and the signal coverage of these networks overlaps each other, forming the heterogeneous wireless network area. Network selection algorithm is the key technology of heterogeneous wireless network. The common network selection algorithms are based on accurate network attribute values. However, due to the mobility of users, the interference of wireless signals and the fluctuation of network state, the network attributes obtained by the algorithms are often uncertain. To solve this problem, this paper designs a multi-attribute access selection approach based on the fuzzy network attributes. This approach calculates the network attribute values by interval hesitant fuzzy theory at first. Then, it calculates the subjective weights of network attribute values by the analytic hierarchy process and the objective weights of network attribute values by the entropy method. The integrated weights of subjective weights and objective weights are obtained by the method based on the longest geometric distance to the negative ideal solution. In the end, we calculate the scores of candidate networks by grey relational analysis based on the intuitionistic fuzzy decision matrix. The simulation shows that the algorithm proposed by this paper can select the most suitable network and reduce the number of handoffs under the environment of uncertain network attribute values.