[Paper Review] Use of the Triangular Fuzzy Numbers for Student Assessment

Michael Gr. Voskoglou|arXiv (Cornell University)|Jul 12, 2015

Multi-Criteria Decision Making9 references10 citations

TL;DR

This paper proposes a fuzzy assessment method using triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TpFNs) for student evaluation, integrating a center of gravity (COG) defuzzification technique to enable reliable comparison between student groups. The approach provides a more robust linguistic and quantitative assessment framework by overcoming the non-comparability issue of fuzzy numbers in educational evaluation.

ABSTRACT

In an earlier work we have used the Triangular Fuzzy Numbers (TFNs)as an assessment tool of student skills.This approach led to an approximate linguistic characterization of the students' overall performance, but it was not proved to be sufficient in all cases for comparing the performance of two different student groups, since tywo TFNs are not always comparable. In the present paper we complete the above fuzzy assessment approach by presenting a defuzzification method of TFNS based on the Center of Gravity (COG) technique, which enables the required comparison. In addition we extend our results by using the Trapezoidal Fuzzy Numbers (TpFNs) too, which are a generalization of the TFNs, for student assessment and we present suitable examples illustrating our new results in practice.

Motivation & Objective

• To address the limitation of triangular fuzzy numbers (TFNs) in comparing student performance across groups due to non-comparability.
• To develop a defuzzification method based on the Center of Gravity (COG) technique to enable meaningful comparison of fuzzy assessment results.
• To extend the fuzzy assessment framework by incorporating trapezoidal fuzzy numbers (TpFNs), which generalize TFNs and offer greater flexibility.
• To demonstrate the practical applicability of the proposed method through illustrative examples in student assessment.

Proposed method

• The paper employs triangular fuzzy numbers (TFNs) to represent students' performance in a linguistic and fuzzy manner, capturing uncertainty in assessment.
• It introduces a defuzzification process using the Center of Gravity (COG) technique to convert fuzzy numbers into crisp values for comparison.
• The COG method computes the centroid of a TFN, providing a single numerical value that represents the fuzzy assessment outcome.
• The approach is extended to trapezoidal fuzzy numbers (TpFNs), which generalize TFNs by allowing a flat top, increasing representational flexibility.
• The method is applied to real-world student assessment data, with examples illustrating the transformation and comparison process.
• The comparison of student groups is performed using the defuzzified crisp values derived from COG, enabling objective ranking and evaluation.

Experimental results

Research questions

• RQ1 Can the Center of Gravity (COG) technique effectively defuzzify triangular fuzzy numbers (TFNs) to enable reliable comparison of student performance?
• RQ2 How does the use of trapezoidal fuzzy numbers (TpFNs) improve the assessment model compared to TFNs in educational evaluation?
• RQ3 To what extent does the proposed defuzzification method overcome the non-comparability issue of fuzzy numbers in student assessment?
• RQ4 What are the practical implications of applying fuzzy logic with COG defuzzification in real student assessment scenarios?

Key findings

• The COG defuzzification method successfully transforms triangular fuzzy numbers into crisp values, enabling valid and reliable comparison between student groups.
• The use of trapezoidal fuzzy numbers (TpFNs) provides a more flexible representation of student performance than TFNs, especially when performance spans a range of values.
• The proposed method allows for a more nuanced and accurate assessment of student performance by incorporating linguistic uncertainty and fuzzy reasoning.
• The illustrative examples demonstrate that the defuzzified results align with intuitive expectations in student group comparisons.