We propose two fuzzy co-clustering algorithms based on the double Kmeans algorithm. Fuzzy approaches are known to require more computation time than hard ones but the fuzziness principle allows a description of uncertainties that often appears in real world applications. The first algorithm proposed, fuzzy double Kmeans (FDK) is a fuzzy version of double Kmeans (DK). The second algorithm, weighted fuzzy double Kmeans (W-FDK), is an extension of FDK with automated variable weighting allowing co-clustering and feature selection simultaneously. We illustrate our contribution using Monte Carlo simulations on datasets with different parameters and real datasets commonly used in the co-clustering context.