Time-varying classifiers, namely, evolving classifiers, play an important role in a scenario in which information is available as a never-ending online data stream. We present a new unsupervised learning method for numerical data called evolving Internal-eXternal Fuzzy clustering method (Fuzzy eIX). We develop the notion of double-boundary fuzzy granules and elaborate on its implications. Type 1 and type 2 fuzzy inference systems can be obtained from the projection of Fuzzy eIX granules. We perform the principle of the balanced information granularity within Fuzzy eIX classifiers to achieve a higher level of model understandability. Internal and external granules are updated from a numerical data stream at the same time that the global granular structure of the classifier is autonomously evolved. A synthetic nonstationary problem called Rotation of Twin Gaussians shows the behavior of the classifier. The Fuzzy eIX classifier could keep up with its accuracy in a scenario in which offline-trained classifiers would clearly have their accuracy drastically dropped.