As the environment and information-technology conditions of the Internet of Things matured, various applications were launched. In education, e-learning is promoted so that students' learning is no longer restricted to the classroom. E-learning schedules are flexible, and learners' commuting costs are low. Apparently, improving the quality of e-learning systems can enhance learners' learning effectiveness, satisfaction, engagement, and learning efficacy. A performance evaluation matrix is a

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... ul tool for collecting users' opinions to assess the performance of an operating system, and it is widely used to evaluate and improve performance in numerous industries and organizations. Therefore, this study used this matrix to construct a model for evaluation and analysis, providing suggestions on improving e-learning systems. This approach maintained the simple response model of Likert scales, which increases the efficiency and accuracy of data collection. Furthermore, the fuzzy membership function of the discriminant index was constructed based on the confidence interval, thereby solving the problems of sampling error and the complexity of collecting fuzzy linguistic data. Besides, we simplified calculations by standardizing test statistics to increase evaluation efficiency. As a result, this study improved the quality of e-learning system, enhanced users' learning effectiveness, satisfaction, and engagement, and achieved the goal of sustainability.