N-EDU: An Innovative Neutrosophic Logic Construction for Digital Transformation Effectiveness of College Ideological and Political Education with Mathematical Foundations and Applied Learning Dynamics

Abstract

This paper presents N-EDU, a new mathematical framework for Digital Ideological and Political Education (DIPE) based on neutrosophic logic. In N-EDU, both learners and educational content are described using neutrosophic triplets (  ), where  is the degree of truth,  is the degree of uncertainty, and  is the degree of falsehood. We define two main operators: a fusion operator for combining content with a learner's current knowledge, and a debias operator for reducing misinformation. We also design a continuity gate using neutrosophic topology to prevent sudden increases in uncertainty during the learning process. The framework includes formal definitions, mathematical proofs, and case studies. Results show that N-EDU can increase truth, reduce falsehood, and keep uncertainty stable while remaining interpretable and practical for real-world use.