Abstract: Based on the interval-valued q-Rung orthopair fuzzy environment and the Frank operator, some operation rules of the interval-valued q-Rung orthopair fuzzy Frank operator are defined, the interval-valued q-Rung orthopair fuzzy Frank weighted average operator (IVq-ROFFWA) and the weighted geometric operator (IVq-ROFFWG) are proposed based on the research of their idempotency, boundedness and monotonicity. Then, a multi-attribute group decision method (MAGDM) based on the IVq-ROFFWA operator is proposed, which selects the value of q satisfying requirements and obtains the target interval-valued fuzzy numbers by the IVq-ROFFWA, compares their scores to obtain the optimal solution, and also proposes that different q values do not affect the optimal solution ranking. Finally, the IVq-ROFFWA operator based multi-attribute group decision making method is verified to be feasible and effective. It is also verified that different q values do not affect the optimal solution ordering. The comparative analysis shows that the group decision methods based on IVq-ROFFWA and IVq-ROFFWG operators are consistent with the group decision methods based on other operators.

Key words: interval-valued, q-Rung orthopair fuzzy, Frank operator, group decision making