A Neutrosophic TwoFold Algebraic Framework for Modeling Uncertainty in University English Teachers' Development Competence in the Era of Big Data

In today's world, big data has changed the way we understand and measure teaching. For university English teachers, it is no longer easy to evaluate their true teaching performance. The information we collect about them can be uncertain, incomplete, or even confusing. Traditional methods do not fully capture this complexity. This study presents a new mathematical model based on Neutrosophic TwoFold Algebra. It allows us to represent each teaching skill with three parts. These are the degree of truth, the degree of uncertainty, and the degree of falsity. Together, they describe how much a teacher really has that skill, how unclear it is, and how much the skill is missing. We also introduce a new TwoFold operation. It combines two skills into one using a special formula. This formula includes mathematical operations that reflect how skills interact in real teaching environments where data is often mixed or unreliable. The model is designed to work with real educational data, even when that data is not perfect. This approach helps us better understand a teacher’s full competence. It brings more accuracy to the evaluation process in a time when digital tools, online learning, and large data systems are everywhere.