Fuzzy Logic-Driven Assessment Model for Mathematical Proof Grading in Education

Abstract

Fuzzy logic has become a critical tool in handling uncertainty in decision-making systems, especially those that require subjective human judgment. This paper aims to introduce an advanced fuzzy logic-based grading system for evaluating mathematical proofs with improved consistency, flexibility, and automation of grading processes in mathematical education. This study proposes a refined fuzzy logic system implemented in Python to assess the correctness of students’ proofs based on four core questions: assumptions and conclusions, correct definitions, appropriate proof methods, and logical reasoning. The proposed system utilized the fuzzy logic technique of fuzzification, rule based inference, and defuzzification to evaluate a score between ”Correct” and ”False” in points from 0 to 10. The system was tested using student data while fuzzy grades were assessed together with the grades assigned by the professor. The results show that the system provides a subtler and more reliable grading procedure, which handles partial correctness better than the traditional binary methods. It addresses the gap in grading the mathematical proof by introducing an adaptive, computationally efficient, and consistent solution.