A Neutrosophic Number System for Modeling Ambiguity and Conflict in Industry-Education Collaboration for Vocational College Talent Cultivation - Lingjie Sun; Jingyang Cai; Chunlei Gao (Neutrosophic Sets and Systems)
t: In this paper, we introduce an original neutrosophic number system designed to model ambiguity, indeterminacy, and contradiction in real-world decision-making environments. Motivated by the complex interactions within industry-education integration for vocational colleges, the proposed system captures multi-perspective evaluations and conflicting stakeholder opinions through mathematically defined truth, indeterminacy, and falsity degrees. We define the neutrosophic number as a triple structure (T,I,F), and we present a novel set of arithmetic operations, equivalence relations, and algebraic properties tailored to this structure. To illustrate the applicability and strength of the proposed framework, we develop multiple examples involving collaborative talent cultivation, such as student assessment, industry feedback, and curriculum alignment. Each example is fully constructed with numerical calculations, logical reasoning, and neutrosophic algebraic rules. In addition, we propose evaluation matrices, contradiction metrics, and decision-support formulations grounded in the new system. Our approach offers a mathematically rigorous and logically expressive framework for modeling uncertainty, inconsistency, and partial agreement in educational collaboration contexts. This research contributes to both theoretical mathematics and practical modeling, establishing a robust foundation for neutrosophic decision processes in vocational talent development.