The p, q, r-spherical fuzzy set represents a recent advancement in fuzzy set theory, offering improved flexibility and realism for managing uncertainty in decision-making processes. Membership degrees in p, q, r-spherical fuzzy sets are typically represented as single-point real numbers. In this paper, we introduce interval-valued p, q, r-spherical fuzzy sets ( \({\textrm{IV}}_{{(p,q,r)}}{\textrm{SFSs}}\) ) as an extension of p, q, r-spherical fuzzy sets. \({\textrm{IV}}_{{(p,q,r)}}{\textrm{SFSs}}\) feature membership, neutral membership, and non-membership functions expressed as intervals rather than single-point real numbers. \({\textrm{IV}}_{{(p,q,r)}}{\textrm{SFSs}}\) feature three parameters (p, q, and r) that regulate the influence of membership grades in accordance with the requirements of the decision-making process. We establish operational laws and properties for these sets and propose aggregation operators, specifically interval-valued p, q, r-spherical fuzzy weighted averaging and interval-valued p, q, r-spherical fuzzy weighted geometric operators, to handle interval-valued information. The traditional TOPSIS method is extended to address real-life multi-criteria group decision-making problems within the \(\hbox {IV}_{{(p,q,r)}}\) SFS framework. We employ the entropy approach to compute criteria weights, while the Best-Worst method is utilized to determine expert weights. A numerical example concerning the selection of solar energy investment locations is presented to demonstrate the feasibility of our proposed method. Finally, a comparative analysis is conducted to validate the effectiveness of our approach against existing methodologies.
