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Recently, Yang et al. (2019) proposed a fuzzy model-based Gaussian (F-MB-Gauss) clustering that combines a model-based Gaussian with fuzzy membership functions for clustering. In this paper, we further consider the F-MB-Gauss clustering with the least absolute shrinkage and selection operator (Lasso) for feature (variable) selection, termed a fuzzy Gaussian Lasso (FG-Lasso) clustering algorithm. We demonstrate that the proposed FG-Lasso is a good clustering algorithm with better choice for feature subset selection. Experimental results and comparisons actually present these good aspects of the proposed FG-Lasso clustering algorithm. Cancer is a disease with growth of abnormal cells in a body. WHO reported that it is the first or second main leading cause of death. It spreads and affects the other parts of body if there is not properly diagnosed. In the paper, we apply the proposed FG-Lasso to cancer data with good feature selection and clustering results.