Emotion detection in the natural language text has drawn the attention of several scientific communities as well as commercial/marketing companies: analyzing human feelings expressed in the opinions and feedback of web users helps understand general moods and support market strategies for product advertising and market predictions. This paper proposes a framework for emotion‐based classification from social streams, such as Twitter, according to Plutchik's wheel of emotions. An entropy‐based weighted version of the fuzzy c‐means (FCM) clustering algorithm, called EwFCM, to classify the data collected from streams has been proposed, improved by a fuzzy entropy method for the FCM center cluster initialization. Experimental results show that the proposed framework provides high accuracy in the classification of tweets according to Plutchik's primary emotions; moreover, the framework also allows the detection of secondary emotions, which, as defined by Plutchik, are the combination of the primary emotions. Finally, a comparative analysis with a similar fuzzy clustering‐based approach for emotion classification shows that EwFCM converges more quickly with better performance in terms of accuracy, precision, and runtime. Finally, a straightforward mapping between the computed clusters and the emotion‐based classes allows the assessment of the classification quality, reporting coherent and consistent results.