Detection of anomalous behaviors in data centers is crucial to predictive maintenance and data safety. With data centers, we mean any computer network that allows users to transmit and exchange data and information. In particular, we focus on the Tier-1 data center of the Italian Institute for Nuclear Physics (INFN), which supports the high-energy physics experiments at the Large Hadron Collider (LHC) in Geneva. The center provides resources and services needed for data processing, storage, analysis, and distribution. Log records in the data center is a stochastic and non-stationary phenomenon in nature. We propose a real-time approach to monitor and classify log records based on sliding time windows, and a time-varying evolving fuzzy-rule-based classification model. The most frequent log pattern according to a control chart is taken as the normal system status. We extract attributes from time windows to gradually develop and update an evolving Gaussian Fuzzy Classifier (eGFC) on the fly. The real-time anomaly monitoring system has to provide encouraging results in terms of accuracy, compactness, and real-time operation.