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Difference systems of sets (DSS) and frequency-hopping sequences (FHS) are two objects with many applications in wireless communication. Zero-difference balanced function (ZDBF) and near zero-difference balanced functions (NZDBF) are two types of functions which can be used to obtain optimal DSSs and FHSs. In order to obtain more optimal DSSs and FHSs, zero-difference function (ZDF) as a generalization of ZDBF and NZDBF was recently proposed. In this paper, four classes of ZDFs with good applications are given from some known ZDBFs. It is noticed that these ZDFs are neither ZDBFs nor NZDBFs. As a result, more optimal DSSs and FHSs with new flexible parameters are obtained.