Type-2 fuzzy set construction and application for adaptive student assessment system

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 (I). 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.