Interval-valued q-rung orthopair fuzzy interactive Dubois–Prade operator and its application in group decision-making

The Dubois–Prade operator can transform its parameter into different values when processing data, which can make it more flexible. Interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) give decision-makers more degrees of freedom. Combining the flexibility of the Dubois–Prade operators and the degrees of freedom of IVq-ROFSs, this paper proposes the interval-valued q-rung orthopair fuzzy Dubois–Prade (IVq-ROFDP) operations and the interval-valued q-rung orthopair Dubois–Prade ordered weighted average (IVq-ROFDPOWA) operator under IVq-ROFSs. Built upon this, considering the interaction between the membership degree and nonmembership degree, the interval-valued q-rung orthopair fuzzy interactive Dubois–Prade (IVq-ROFIDP) operations and the interval-valued q-rung orthopair fuzzy interactive Dubois–Prade ordered weighted average (IVq-ROFIDPOWA) operator are further proposed, and their properties are studied. Finally, a new group decision-making method based on the IVq-ROFIDPOWA operator is proposed to solve the multiattribute group decision-making (MAGDM) problem. The results of two case implementations and the sensitivity analysis show that the proposed operator and group decision-making method are feasible and effective. Furthermore, the comparative analysis shows that the group decision-making method proposed in this paper can better reflect the differences between alternatives.