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Fuzzy relationships exist between students' learning performance with various abilities and a test item. However, the challenges in implementing adaptive assessment agents are obtaining sufficient items, efficient and accurate computerized estimation, and a substantial feedback agent. Additionally, the agent must immediately estimate students' ability item by item, which places a considerable burden on the server, especially for a group test. Hence, the implementation of adaptive assessment agent is more difficult in practice. This paper proposes an agent with particle swarm optimization (PSO) based on a Fuzzy Markup Language (FML) for students' learning performance evaluation and educational applications, and the proposed agent is according to the response data from a conventional test and an item response theory (IRT)-based three-parameter logistic (3PL) model. First, we apply a Gauss-Seidel (GS)-based parameter estimation mechanism to estimate the items' parameters according to the response data, and then to compare its results with those of an IRTbased Bayesian parameter estimation mechanism. In addition, we propose a static-IRT test assembly mechanism to assemble a form for the conventional test. The presented FML-based dynamic assessment mechanism infers the probability of making a correct response to the item for a student with various abilities. Moreover, this paper also proposes a novel PSO-based FML (PFML) learning mechanism for optimizing the parameters between items and students. Finally, we adopt a K-fold cross validation mechanism to evaluate the performance of the proposed agent. Experimental results show that the novel PFML learning mechanism for the parameter estimation and learning optimization performs favorably. We believe the proposed PFML will be a reference for education research and pedagogy and an important co-learning mechanism for future human-machine educational applications. Index Terms-Dynamic assessment, Fuzzy Markup Language (FML), Genetic FML (GFML), item response theory (IRT), particle swarm optimization (PSO)The authors would like to thank the financial support sponsored by 1) Ministry

Student's performance is classified into four levels, including below basic, basic, proficient, and advanced levels. The descriptions of the performance standard make students understand their learning achievement via percentile rank (PR), a norm-referenced score, and T score (T). This paper develops an adaptive student assessment system and invites elementary-school students to do a test in mathematics. Additionally, one adaptive item selection strategy mechanism is developed to choose next item that meets the student's current estimated ability. After that, the response data are collected to execute the type-2 fuzzy set (T2FS) construction mechanism to build a personalized T2FS for each student's performance and a T2FS for all students with an identical level. Finally, the student evaluation mechanism is executed to show students and teachers some useful information to assist in their future teaching and guidance. The simulation results show the proposed approach is feasible to adaptively select items from the item bank and construct T2FS for students' ability. In the future, we plan to use the technologies of optimization and computational intelligence to infer each student's ability in the test based on the constructed T2FSs.