A multi-level five-way decision framework using spherical fuzzy rough sets for complex choices in digital circular supply networks

Circular supply networks represent a broad and well researched field, with significant study dedicated to the challenges of their establishment. However, research on the impacts within government managed circular supply chains remains limited. Consequently, there is still a lack of understanding regarding how digital technologies can help overcome these specific challenges in the public sector's transition to circularity. In this work, we develop a multi level decision model based on five distinct pathways to handle complex decision-making scenarios with high accuracy. We employ spherical fuzzy sets (S_pFS), which offer greater tolerance and adaptability in capturing vague information compared to intuitionistic and Pythagorean fuzzy sets. Within the S_pFS framework, the three-dimensional membership functions enable decision-makers to improve judgment under uncertainty. Digital circular supply chain decision systems particularly in transportation can be structured using the five-way decision (5WD) concept with spherical fuzzy (S_pF) information. The proposed model classifies criteria across multiple levels and evaluates their positions using decision-theoretic fuzzy rough sets (DTRFS) and the spherical weighted arithmetic mean (S_pWAM). This study advocates the use of S_pF data alongside stable ranking and structured classification algorithms to support decision-making in complex, ambiguous situations. A numerical example is provided to illustrate the applicability of the algorithm, tested across five distinct decision scenarios to validate the model's accuracy. Statistical assessments confirm the strong performance of the proposed framework.