Unlearning has significant application value in safeguarding privacy, mitigating the impact of contaminated samples, and processing redundant data. However, existing unlearning methods are mostly applied to black-box models such as neural networks, while achieving efficient single-class and multi-class unlearning in interpretable TSK fuzzy classification systems remains challenging. To address this, this study proposes a TSK fuzzy unlearning method for classification (TSK-FUC). First, the rule base is divided into three subsets using the normalized activation strengths of rule antecedent parameters on the (single/multi-class) forgotten data: 1) a deleted rule set that is highly relevant to the forgotten data, 2) a retained rule set with low relevance to the forgotten data, and 3) an updated rule set showing overlapping relevance to both the retained and forgotten data. Subsequently, differential processing strategies are applied: the deleted rule set is directly removed to eliminate major information residues and reduce the number of system parameters; the retained rule set is fully preserved to reduce parameter adjustment scope during unlearning; and for the updated rules, class-specific noise is added to the consequent parameters to further eliminate information related to the forgotten data, thus achieving single-class and multi-class unlearning. Experimental results on 16 benchmark datasets demonstrate that TSK-FUC accurately partitions the rule space and exhibits effective single-class and multi-class unlearning performance through differentiated processing in both 0-order and 1-order established TSK fuzzy classification systems. This method maintains the interpretability of the rule base while rendering the TSK fuzzy classification system more lightweight in terms of structure after unlearning.