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Evolving fuzzy rule-based structures represent extremely powerful methods for online classification of data streams. The fuzzy rules are generated, modified and removed automatically in these systems. One of the simplest but efficient algorithms of this type is evolving classifier (eClass) that constructs the rules without any prior knowledge, starting “from scratch”. However, this algorithm cannot cope properly with drift and shift in the concept of data. In this paper, we propose a new efficient online method to increase the performance of this algorithm by setting a suitable weight for each rule and handle the drift and shift in the concept of data. By adjusting proper weights, the zone of influence of each rule can be easily controlled and changed regarding the restyling of the environment. Our weight adjusting algorithm is based on an efficient batch mode weight adjusting method that is developed to be consistent with characteristics of data streams. The proposed algorithm is evaluated on some standard data sets of UCI Repository and some real world data streams, and compared with the eClass algorithm. The results show that the proposed algorithm outperforms the eClass approach, and has significant improvement in most cases.