With respect to multi-attribute group decision making, in this study two induced continuous Choquet integral operators named as the induced continuous Choquet weighted averaging (ICCWA) operator and the induced continuous Choquet geometric mean (ICCGM) operator are defined, which reflect the interactive characteristics between elements. Meantime, some associated desirable properties are studied to provide assurance in applications. In order to globally reflect the interactions between elements, we further define the probabilistic generalized semivalue ICCWA (PGS-ICCWA) operator and the probabilistic generalized semivalue ICCGM (PGS-ICCGM) operator. If the information about the weights of experts and attributes is incompletely known, the models for the optimal fuzzy measures on experts set and on attribute set based on consistency principle and TOPSIS method are respectively established. Moreover, an approach to uncertain multi-attribute group decision making with incomplete weight information and interactive conditions is developed. Finally, a numerical example is provided to illustrate the practicality and feasibility of the developed procedure.