The well-known generalisation of hard c-means (HCM) clustering is fuzzy c-means (FCM) clustering where a weight exponent on each fuzzy membership is introduced as the degree of fuzziness. An alternative generalisation of HCM clustering is proposed in this paper. This is called fuzzy entropy (FE) clustering where a weight factor of the fuzzy entropy function is introduced as the degree of fuzzy entropy. The weight factor is similar to the weight exponent and has a physical interpretation. The noise clustering approach, the fuzzy covariance matrix and the fuzzy mixture weight are also proposed. Moreover, we can show Gaussian mixture clustering is regarded as a special case of FE clustering. Some illustrative examples are performed on the Butterfly and Iris data.