A Neutrosophic Number System for Modeling Ambiguity and Conflict in Industry-Education Collaboration for Vocational College Talent Cultivation

Abstract

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. 

DOI: 10.5281/zenodo.15843794