Application of Fuzzy Numbers to Assessment Processes

The proper system for evaluating the learning achievement of students is the key to realizing the purpose of education. In recent years, several methods have been presented for applying the fuzzy set theory in the educational grading systems. In this paper, we propose a method for the evaluation of students’ answerscripts using a fuzzy system. The proposed system applies fuzzification, fuzzy inference, and defuzzification in considering the difficulty, the importance and the complexity of questions. The transparency, objectivity, and easy implementation of the proposed fuzzy system provide a useful way to automatically evaluate students’ achievement in a more reasonable and fairer manner.  2008 Elsevier Ltd. All rights reserved.

Education Sciences, 2013

Fuzzy logic, which is based on fuzzy sets theory introduced by Zadeh in 1965, provides a rich and meaningful addition to standard logic. The applications which may be generated from or adapted to fuzzy logic are wide-ranging and provide the opportunity for modeling under conditions which are imprecisely defined. In this article we develop a fuzzy model for assessing student groups' knowledge and skills. In this model the students' characteristics under assessment (knowledge of the subject matter, problem solving skills and analogical reasoning abilities) are represented as fuzzy subsets of a set of linguistic labels characterizing their performance, and the possibilities of all student profiles are calculated. In this way, a detailed quantitative/qualitative study of the students' group performance is obtained. The centroid method and the group's total possibilistic uncertainty are used as defuzzification methods in converting our fuzzy outputs to a crisp number. According to the centroid method, the coordinates of the center of gravity of the graph of the membership function involved provide a measure of the students' performance. Techniques of assessing the individual students' abilities are also studied and examples are presented to illustrate the use of our results in practice.

2014

We apply a Triangular Fuzzy Model (TFM) for assessing students' problem solving skills. The TFM is a variation of a special form of the Centre of Gravity (COG) defuzzification technique that we have used in earlier papers for assessing students' performance in several mathematical tasks. The main idea of the TFM is the replacement of the rectangles appearing in the graph of the COG technique by isosceles triangles sharing common parts. In this way we cover the ambiguous cases of students' scores being in the limits between two successive grades (e.g. between A and B). A classroom experiment is also presented illustrating our results in practice.

Journal of Information System and Technology Management, 2022

The education system in Malaysia employs classical method in evaluation students' progress performances during their foundation level. The result was obtained by adding all the assessments scored and was graded based on grade A, A-, B+, B, …, and F. Somehow, non-classical methods may be applied such as fuzzy logic, where it can be applied to many forms of decision making. This paper proposed evaluation on students' performances by using fuzzy logic approach. The assessment score obtained based on their assignment, midterm examination and final term examination of 26 Agriscience students, in Preparatory Centre for Science and Technology (PPST), University Malaysia Sabah, UMS was carried out with fuzzy logic. Their results are calculated based on classical method and fuzzy logic approach, which is then compared and analysed. The comparison shows variation between classical and fuzzy logic approach in terms of their overall results.

2012

results give motivation and encouragement to the students. So reforms in education are must not only in curriculum development but also in students" performance assessment. Proposed method is useful when questions in the examination are of subjective or objective type and total time duration is given to attempt all questions rather than individual question. This method considers importance and complexity of question into account. It makes use of fuzzy inference system (FIS) and fuzzy logic.

Physical and Mathematical Education, 2018

Analogical reasoning is a very important part of the human cognition in general for creativity and scientific discovery and in particular it is a very useful method for solving mathematical problems by retrieving from the memory similar problems solved in the past and adapting their solutions for use with the target problem. On the other hand, the student assessment is an essential task of Education, because, apart of being a social need and demand, it helps the instructors in designing their future plans for a more effective teaching procedure. However, frequently an instructor is not sure about the exact grade corresponding to each student's performance. Therefore, the student assessment is characterized by a degree of vagueness and/or uncertainty. Consequently, fuzzy logic, due to its property of characterizing the ambiguous real life situations with multiple values, becomes a reach resource of assessment techniques to be applied in such vague cases. In this work fuzzy relation equations are used as a tool for evaluating student analogical problem solving skills. The fuzzy relation equations are obtained by the composition of binary fuzzy relations, which are fuzzy sets defined on the Cartesian product of two crisp sets. The compositions of binary fuzzy relations are conveniently performed in terms of the membership matrices of them. The same elements of the membership matrices are used in these compositions as would be used in the regular multiplication of matrices, but the product and sum operations are here replaced with the min and max operations respectively. The notion of fuzzy relation equations was first proposed by Sanchez in 1976 and later was further investigated by other researchers. A classroom application and other suitable examples are also presented in this article illustrating our results. Further, the present work is connected to our earlier research efforts on utilizing several other fuzzy Logic techniques as tools for the assessment of the student performance.

IEEE Transactions on Education, 1995

The difficulties associated with translating a set of scores into letter-grades are discussed. A novel method for automating this process, the Fuzzy Grading System, is developed and compared to traditional practices. Letter-grades are recognized to be f u u y descriptors of students' performance. Thus, operations aimed at defining letter-grade bouhdaries are naturally carried out in the context of fuzzy set theory and logic. The Fuzzy Grading System utilizes students' and instructor's performance measures in order to m d i y a set of collectively approved, a priori fuzzy grades, so as to produce a "fair" mark distribution. The validity of grades is increased by compensating for factors that are not directly accessible to simpler, traditional grading methods.

In this paper, we discuss the analysis of students' evaluation, especially in the case of the students' answerscripts under the evaluation grade of linguistic data. We transfer mostly linguistic data, subjective message into triangular fuzzy numbers, and use the function principle instead of the extension principle to calculate the students' score. In addition to, we use the degree of similarity between two fuzzy numbers with the utility value of fuzzy number to transfer the students' score into letter-grade score.

2019

Learning assessments of students are very vital in assessing the overall learning performance of students. Knowing the learners capabilities are always part of a teacher’s job to fully understand the learner’s need. Hence, the researchers were motivated to conduct this study on the purpose of evaluating and identifying the performance of students using the fuzzy inference. The research is focusedonthe private university students.Results of examinations from both the lecture and laboratory classes are evaluated to determine the how the student performs in a class. The exam scores of lecture and laboratory class serves as input to the fuzzification technique to determine which among the two class types would the students perform well. In this paper, fuzzy logic basic concepts are applied on theexam results. The authors then concluded that students are performing better during laboratory examinations.

2014

In this paper we develop a method for assessing the overall performance of groups of individuals participating in any kind of human activities. For this, we represent each of the group under assessment as a fuzzy subset of a set U of linguistic labels characterizing its members' performance and we apply a recently developed Trapezoidal Fuzzy Assessment Model (TRFAM) for converting the fuzzy data collected from the corresponding activity to a crisp number. The TRFAM is a variation of the popular in fuzzy mathematics centre of gravity (COG) defuzzification technique, which has been properly adapted and used as an assessment method in earlier papers. According to the TRFAM the higher is an individual's performance the more its "contribution" to the corresponding group's overall performance (weighted performance). Two real life applications are also presented, related to the bridge players' performance and to the students' assessment respectively, illustrat...