This paper presents the sequel of evolving fuzzy rule-based classifier eClass, called here as simplified evolving classifier, simpl_eClass. Similarly to eClass, simpl_eClass comprises of two different classifiers, namely zero and first order (simpl_eClass0 and simpl_eClass1). The two classifiers differ from each other in terms of the consequent part of the fuzzy rules, and the classification strategy used. The design of simpl_eClass is based on the density increment principle introduced recently in so called simpl_eTS+ approach. The rule learning in simpl_eClass does not involve computation of potential values that allows it to attain computationally much less expensive model update phase compared to eClass. As compared to other FRB classifiers, it retains all the advantages of eClass, such as being on-line and evolving, having zero and first order. In comparison with other non-fuzzy classifiers it has the advantage of interpretability and transparency (especially zero order type). The goals of this paper are to demonstrate the applicability of simpl_eTS+ to classification task, and to empirically show that the simplification of eClass to simpl_eClass by using potential-free approach does not compromise the accuracy of the classifiers. In order to attain the goals, the classifiers are tested by performing several experiments using benchmark data sets. The simpl_eClass1 classifier is also applied to the real-life problem of on-line scene categorization for low-resource devices benefiting from its low computational cost. The results obtained from the experiments endorse that simpl_eClass achieves the accuracy of eClass while simplifying rule learning process.