Pythagorean multi-fuzzy N-soft sets: a novel hybrid model for group decision making and its applications in distance education

The rapid development of distance education has led to a pressing need for practical evaluation of learning platforms, especially in situations where decision-making involves multiple evaluators and uncertain information. To address this need, we introduce a new hybrid model called Pythagorean Multi-Fuzzy N-Soft Sets (PMFNSS). This model is designed to improve group decision-making under complex and ambiguous conditions. The proposed PMFNSS model was built by combining Pythagorean Fuzzy N-Soft Sets (PFNSS) and Multi-Fuzzy N-Soft Sets (MFNSS). First, we formally defined the concept of PMFNSS. Next, we proposed a group decision-making algorithm based on the framework. Finally, to validate its applicability, the model was used in a real-life case study on the evaluation of digital learning platforms in distance education. The results indicated that PMFNSS can serve as a multi-attribute group decision-making tool. Its application to distance education offers a systematic approach to evaluating and optimizing digital learning platforms for resource efficiency and sustainability.