A fuzzy inference system-based criterion-referenced assessment model

The main aim of criterion-referenced assessment (CRA) is to report students' achievements in accordance with a set of references. In practice, a score is given to each test item (or task). The scores from different test items are added together and then projected or aggregated, usually linearly, to produce a total score. Each component score can be weighted before being added together in order to reflect the relative importance of each test item. In this paper, the use of a fuzzy inference system (FIS) as an alternative to the conventional addition or weighted addition in CRA is investigated. A novel FIS-based CRA model is presented, and two important properties, i.e., the monotonicity and sub-additivity properties, of the FIS-based CRA model are investigated. A case study relating to assessment of laboratory projects in a university is conducted. The results indicate the usefulness of the FIS-based CRA model in comparing and assessing students' performances with human linguistic terms. Implications of the importance of the monotonicity and sub-additivity properties of the FIS-based CRA model in undertaking general assessment problems are discussed.

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