We define the notion of weak universal integral based on a semicopula, and introduce and discuss two particular classes of weak universal integrals based on semicopulas, which generalize the well-known Sugeno and Shilkret integrals. In special cases, when the considered semicopulas are bounded from above by the Łukasiewicz t-norm, all introduced integrals reduce to the corresponding smallest semicopula based universal integrals. Remarkably, when the product semicopula is considered, the proposed integrals generalizing the Shilkret integral belong to the class of aggregation functions, which is not the case of the minimum semicopula when the introduced integrals generalize the Sugeno integral.

我们定义了基于半算子的弱泛积分的概念，并介绍和讨论了基于半算子的两类特殊的弱泛积分，它们概括了著名的Sugeno和Shilkret积分。在特殊情况下，当所考虑的半算子由Łukasiewiczt范式从上方界定时，所有引入的积分都会减少为相应的最小的基于半算子的通用积分。值得注意的是，当考虑乘积半copula时，拟议的推广Shilkret积分的积分属于聚合函数的类别，当引入的积分推广Sugeno积分时，最小半copula不是这种情况。