It is well-known that outliers and noisy data can be very harmful when applying clustering methods. Several fuzzy clustering methods which are able to handle the presence of noise have been proposed. In this work, we propose a robust clustering approach called F-TCLUST based on an “impartial” (i.e., self-determined by data) trimming. The proposed approach considers an eigenvalue ratio constraint that makes it a mathematically well-defined problem and serves to control the allowed differences among cluster scatters. A computationally feasible algorithm is proposed for its practical implementation. Some guidelines about how to choose the parameters controlling the performance of the fuzzy clustering procedure are also given.