Fuzzy membership function and inference-based model for predicting student's knowledge performance

Intelligent Tutoring Systems (ITSs) are special classes of E-learning systems designed to provide adaptive and personalized tutoring based on the individuality of students. The student model is an important component of an ITS that provides the base for this personalization. During the course of interaction between student and the system, a quantitative representation of the actual student‟s characteristics such as the student‟s knowledge state is created based on the observations and predictions the ITS made on each student. The student‟s knowledge is one of the most dynamic characteristic of the student; so dynamic like a moving target. However, modeling student‟s knowledge and diagnosis are complex processes that are characterized by uncertainty and imprecision issues that affect the prediction of the student model. Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory. Its methodology provides a definitive solution to problems of information that may be construed as uncertain or imprecise. A major gap in the existing approach is the absence of an important component of a fuzzy logic controller, the membership function graph which is vital for the management of uncertainty and imprecision in student's knowledge modeling. Moreover, the prediction accuracies of 36% and 90% achieved by the existing models is seen as another limitations in their performance. This study propose novel fuzzy based membership functions and inference mechanisms to design a fuzzy logic based control process which aimed at modeling student's knowledge performance and further diagnosis. Successful design of this two vital fuzzy logic engines will respectively enables the realization of more accurate fuzzy student models and the necessary diagnosis on them. An approximate student model based on fuzzy membership function approach enables making accurate predictions about the state of student's knowledge. The main idea of proposing a novel fuzzy inference process is to provides the necessary diagnosis on the propose fuzzy student model. The inference process take outputs of a fuzzification process with membership functions as input variables for a mechanism which is defined by fuzzy If-Then rules and logical operators, and then reaches the output space that produces a human like decision by inferring on the propose fuzzy student models. For the purpose of this research, the training data which is an instance of students knowledge test performances were obtained from an adaptive-courseware E-learning system that administered knowledge tests to thirty, first year undergraduate students, from two southeastern European Universities, University of split Croatia and University of Mostar Bosnia-Herzegovina in the domain of “computer as a system” comprising of seventy three domain concepts. The results of this knowledge test, the students‟ scores in each of the seventy three domain concepts is to be used as crisp inputs to the proposed fuzzy membership functions to enables the realization of the first fuzzy logic control process, the fuzzification process. The propose membership functions are designed using multi fuzzy terms "poor", "weak", "average", "good", "very good" and "excellent" to allow for adequate fuzzy sets that can capture all intervals in the distribution. However, we need to compare the performance of the propose model with that of the two previous or existing models. With the first model that has 36% accuracy, this comparison is direct as it was implemented using same training data with the propose model. But with second model that has 90% accuracy, this comparison cannot be made directly as it was implemented using different training data with the propose model. This study therefore re-implement the second model using the training data from the domain of “computer as a system” in order to justify the performance of the propose model. The result has shown that the propose method has successfully improved the accuracies of the two previous models.

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