Neutrosophic Network Flow with Truth, Indeterminacy, and Falsity Capacities: An Innovative Mathematical Framework for Efficiency Evaluation of Achievement Transformation of College Student Innovation and Entrepreneurship Training Programs

Abstract

This paper introduces a new mathematical framework that combines neutrosophic logic 
and network flow theory to improve the design of student innovation and 
entrepreneurship training programs. In the proposed approach, each connection in the 
training process is represented as a directed edge with three separate capacities: truth, 
indeterminacy, and falsity. These capacities describe how much confirmed learning, 
uncertainty, and failure can pass between stages of the program. By applying 
conservation rules for each component and adapting classical flow optimization methods, 
we can identify training paths that increase confirmed learning while reducing 
uncertainty and limiting the spread of failure. The framework also extends the max
flow/min-cut theorem to the neutrosophic setting, allowing rigorous analysis under 
incomplete or contradictory data. A fully worked case study with synthetic student data 
shows how the model can guide curriculum adjustments, demonstrating measurable 
improvements in training effectiveness. This work opens a new research direction by 
linking neutrosophic probability with flow networks, offering a versatile tool for decision
making in complex educational systems. 

DOI: 10.5281/zenodo.16888188