some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail. The absolute continuity and singularity of set functions on T∞-tribe are discussed. The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets. As a result, some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation, the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe. In addition, two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.