Summary: The authors point out and correct errors in the paper [He Ming, The double-induced mapping on the \(L\)-fuzzy set, Kexue Tongbao 31, No. 6, p. 475 (1986)]. Then they generalize the concept of double-induced mapping. The induced mapping of \(f\), \(g_x (x,X_1)\), is defined and its properties are discussed. The notes are of significance when constructing mappings with different properties on a set of high stratum and \(L\)-fuzzy set from mappings on a set of low stratum and ordinary set.