Fuzzy rule interpolation (FRI) enables sparse fuzzy rule-based systems to derive an interpolated conclusion using neighboring rules, when presented with an observation that matches none of the given rules. The efficacy of FRI has been further empowered by the recent development of weighted FRI techniques, particularly the one that introduces attribute weights of rule antecedents from the given rule base, removing the conventional assumption of antecedent attributes having equal weighting or significance. However, such work was carried out within the specific transformation-based FRI mechanism. This short paper reports the results of generalizing it through enhancing two alternative representative FRI methods. The resultant weighted FRI algorithms facilitate the individual attribute weights to be integrated throughout the corresponding procedures of the conventional unweighted methods. With systematical comparative evaluations over benchmark classification problems, it is empirically demonstrated that these algorithms work effectively and efficiently using just two nearest neighboring rules.