This paper presents a universal methodology for generating an interval type-2 fuzzy set membership function from a collection of type-1 fuzzy sets. The key idea of the proposed methodology is to designate a specific type-1 fuzzy set as the representative of all input type-1 fuzzy sets. To this end, we use a novel measure of similarity between type-1 fuzzy sets, which relies on both kernel functions and fuzzy information processing methods. Based on the selected representative type-1 fuzzy set, and with respect to the principle of justifiable granularity, an interval type-2 fuzzy set is then formed. The results of the conducted experiments demonstrate the effectiveness of the proposed methodology for generating sound interval type-2 fuzzy sets.