Fuzzy clustering generates a membership vector for each data point in the dataset to indicate its belongingness to different clusters. This procedure can be regarded as an encoding process and the obtained vectors of memberships are the new representations of original data. Naturally, the affinities between new representations or the vectors of memberships should be consistent with the ones between original data points. For example, the data points close to each other should also take similar membership vectors. Such constraints on the affinities of memberships are valuable prior knowledge that should be imposed to the objective function of fuzzy clustering for better performance. To this end, we introduce the membership affinity lasso for fuzzy clustering in this paper. Utilizing alternating direction method of multipliers, an efficient approach is derived to optimize the general membership affinity lasso regularized fuzzy clustering model in offline manner. As illustrative examples, three new fuzzy clustering algorithms with the membership affinity lasso are proposed. Experiments on the synthetic and real data demonstrate the superiority and flexibility of the proposed algorithms.