A GRA approach to a MAGDM problem with interval-valued q-rung orthopair fuzzy information

Interval-valued q-rung orthopair fuzzy numbers (IVq-ROFNs), as a generalization of the q-rung orthopair fuzzy numbers, are a more robust and reliable tool when dealing with uncertain information during decision-making processes, and can therefore be applied to a broader range of situations. This paper presents an approach to a multi-attribute group decision-making (MAGDM) problem in an IVq-ROF environment. In decision-making, the most sensitive part is information fusion (information aggregation); for this purpose, we extend the Einstein geometric aggregation operator for IVq-ROFNs. Einstein operators are valuable in information fusion, as they consider the interrelationship between arguments. Thus, while dealing with the information fusion process, the interrelationship between arguments ensures that aggregated values do not lose information. We use the traditional grey relational analysis (GRA) approach to rank the alternatives based on the attributes. In the GRA approach, we use positive and negative ideal solutions to obtain the grey relational coefficient (GRC). The GRCs of alternatives are calculated based on a new distance measure, which utilizes the hesitancy or indeterminacy degree of IVq-ROFNs. Utilizing the hesitancy or indeterminacy degree in distance measures reduces information loss significantly. The proposed approach considers three cases of attributes' weights: partially known, completely unknown, and known. Consideration of three cases of attributes' weights allows the approach to be applied to any appropriate MAGDM problem. We establish an optimization model to compute partially known attributes' weights; we use the entropy weight determination method to compute unknown attributes' weights. Finally, we discuss a real-world case study to validate the proposed approach.