A Refined Neutrosophic Over/Under Probability Model with Off-Norm Operators for Evaluating the Efficiency of AI-Based Digital Tools in Korean Language Teaching
Keywords:
Neutrosophic probability; over/under probability; off-norm; tool efficiency; Korean language teaching; uncertainty modeling; neutrosophic evaluation; educational measurement.Abstract
This paper presents a new mathematical model based on refined neutrosophic
theory to evaluate the efficiency of AI-based digital tools in Korean language teaching.
The model uses the concept of Over/Under Probability and uses Off-Norm operators to
capture uncertain, inconsistent, or extreme values often found in real classroom data.
Instead of only measuring performance within the traditional range [0,1], our model
allows values greater than 1 or less than 0 to represent over-performance or under
performance. We define precise equations to evaluate both the development and usage
efficiency of educational tools. The model also includes inter-tool synergy using
neutrosophic interaction rules. Two case studies are provided with full calculations to
show how the model works in practice. Compared to traditional evaluation methods, our
neutrosophic model gives deeper insight into tool performance, uncertainty, and
collaboration.
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Copyright (c) 2025 Neutrosophic Sets and Systems
This work is licensed under a Creative Commons Attribution 4.0 International License.
