Performing clustering analysis is one of the important research topics in cancer discovery using gene expression profiles, which is crucial in facilitating the successful diagnosis and treatment of cancer. While there are quite a number of research works which perform tumor clustering, few of them considers how to incorporate fuzzy theory together with an optimization process into a consensus clustering framework to improve the performance of clustering analysis. In this paper, we first propose a random double clustering based cluster ensemble framework (RDCCE) to perform tumor clustering based on gene expression data. Specifically, RDCCE generates a set of representative features using a randomly selected clustering algorithm in the ensemble, and then assigns samples to their corresponding clusters based on the grouping results. In addition, we also introduce the random double clustering based fuzzy cluster ensemble framework (RDCFCE), which is designed to improve the performance of RDCCE by integrating the newly proposed fuzzy extension model into the ensemble framework. RDCFCE adopts the normalized cut algorithm as the consensus function to summarize the fuzzy matrices generated by the fuzzy extension models, partition the consensus matrix, and obtain the final result. Finally, adaptive RDCFCE (A-RDCFCE) is proposed to optimize RDCFCE and improve the performance of RDCFCE further by adopting a self-evolutionary process (SEPP) for the parameter set. Experiments on real cancer gene expression profiles indicate that RDCFCE and A-RDCFCE works well on these data sets, and outperform most of the state-of-the-art tumor clustering algorithms.