Evaluating remote education learning tools: a hybrid decision-support model using rough approximate operators of Fermatean fuzzy rough soft sets

The sudden shift to remote learning has made choosing the best digital tools a crucial challenge for educational institutions, especially in developing areas like Punjab, Pakistan, where infrastructural and resource limitations add extra complexity and uncertainty. Existing multi-attribute decision-making (MADM) models often miss capturing the two-dimensional nature of this uncertainty; including membership and non-membership, while also managing parameterization and data roughness. This study aims to fill this gap by proposing a new combined MADM framework called Fermatean fuzzy rough soft sets (FFRSS) for assessing and selecting remote learning tools. A case study from Punjab, Pakistan, is included, evaluating six popular remote learning tools based on thirteen pedagogically and technically relevant criteria. The criteria weights are calculated using a new fermatean fuzzy entropy method, and the ranking of options is done through the fermatean fuzzy rough soft ring sum product method. Applying the FFRSS model to the case study produces a clear ranking of the remote learning tools. Google Classroom ranks as the most suitable platform, followed by Microsoft Teams and Zoom, with custom Learning Management Systems (LMS) and social media platforms ranking lower. Sensitivity analysis confirms the model's robustness against changes in weights, and comparisons with current methods demonstrate its better handling of high uncertainty. This study presents a tri-integrated model, FFRSS, offering a more adaptable approach to managing complexities in decision-making, especially when choosing educational technology.