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In this paper, based on the definition of the k-quasi-additive fuzzy integral on classical sets, we discuss the properties of k-quasi-additive fuzzy integral on fuzzy sets. Firstly, according to transformation theorems of the integral and the definition of the k-quasi-additive fuzzy integral on fuzzy sets, we give some new properties of k-quasi-additive fuzzy integral on fuzzy sets, so we perfect the properties of the integral. Secondly, based on the definition of the k-quasi-additive fuzzy integrals and transformation theorems, according papers [3-6], we discuss the structural characteristics such as monotony, weak-null-additivity, null-upper-continuity, continuous from above and continuous from below. Furthermore, we discuss the relationships between auto-continuity, uniformly auto-continuity, null-subtractivity, null-additivity, continuous from above and continuous from below and make the relative proof. Finally, we prove some convergence theorems of the k-quasi-additive fuzzy integral on fuzzy sets.
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