Evolving fuzzy classifiers (EFCs) have achieved immense success in dealing with nonstationary data streams because of their flexible characteristics. Nonetheless, most real-world data streams feature highly uncertain characteristics, which cannot be handled by the type-1 EFC. A novel interval type-2 fuzzy classifier, namely evolving type-2 classifier (eT2Class), is proposed in this paper, which constructs an evolving working principle in the framework of interval type-2 fuzzy system. The eT2Class commences its learning process from scratch with an empty or initially trained rule base, and its fuzzy rules can be automatically grown, pruned, recalled, and merged on the fly referring to summarization power and generalization power of data streams. In addition, the eT2Class is driven by a generalized interval type-2 fuzzy rule, where the premise part is composed of the multivariate Gaussian function with an uncertain nondiagonal covariance matrix, while employing a subset of the nonlinear Chebyshev polynomial as the rule consequents. The efficacy of the eT2Class has been rigorously assessed by numerous real-world and artificial study cases, benchmarked against state-of-the-art classifiers, and validated through various statistical tests. Our numerical results demonstrate that the eT2Class produces more reliable classification rates, while retaining more compact and parsimonious rule base than state-of-the-art EFCs recently published in the literature.