Feature selection (FS) is an important data processing technique in the field of machine learning. There have been various FS methods, but all assume that the cost associated with a feature is precise, which restricts their real applications. Focusing on the FS problem with fuzzy cost, a fuzzy multiobjective FS method with particle swarm optimization, called PSOMOFS, is studied in this article. The proposed method develops a fuzzy dominance relationship to compare the goodness of candidate particles and defines a fuzzy crowding distance measure to prune the elitist archive and determine the global leader of particles. Also, a tolerance coefficient is introduced into the proposed method to ensure that the Pareto-optimal solutions obtained satisfy decision makers' preferences. The developed method is used to tackle a series of the UCI datasets and is compared with three fuzzy multiobjective evolutionary methods and three typical multiobjective FS methods. Experimental results show that the proposed method can achieve feature sets with superior performances in approximation, diversity, and feature cost.