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Fuzzy interpolative reasoning is an important inference technique for sparse fuzzy rule-based systems. In this paper, we present a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the areas of fuzzy sets. The proposed method can guarantee the normality and the convexity of the conclusion and can deal with fuzzy interpolative reasoning with complicated membership functions, such as hexagons, polygons and Gaussians. Moreover, the proposed method can deal with the situation when the antecedents and the consequents of fuzzy rules belong to different kinds of membership functions. We use several examples to compare the fuzzy interpolative reasoning results of the proposed method with the ones of the existing methods. The experimental results show that the proposed method is more suitable to deal with fuzzy interpolative reasoning than the existing methods. The proposed method provides a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule-based systems.