Matrix-based approach for knowledge structure construction using variable precision models

Abstract

Assessment of knowledge acquiring and learning is a complex and multidimensional process that involves the evaluation and measurement of an individual's performance in the process of learning and acquiring knowledge. The concept of fuzzy skill encapsulates an individual's latent cognitive abilities and overall competence. In the disjunctive model, an individual must achieve proficiency in at least one relevant skill to solve an item. In contrast, the conjunctive model requires proficiency in all relevant skills. The disjunctive model's excessive leniency and the conjunctive model's excessive rigor have prompted the development of variable precision α-models to mediate between these extremes. Nonetheless, the variable precision α-model warrants further exploration.

Consequently, this paper is conducting a comprehensive analysis of the variable precision α-model, presenting three variants, and examining their respective properties. Additionally, no existing algorithm addresses the construction of the knowledge structure within this model. For this purpose, a new matrix operation is defined, and its properties related to fuzzy skill inclusion degree are investigated. The variable precision model is refined for constructing the knowledge structure, and the corresponding algorithm is designed. Moreover, the applicability of the matrix approach in constructing knowledge structures for variable precision models in the context of dynamic items is examined. Finally, a dataset is used to empirically evaluate the feasibility and effectiveness of the proposed algorithm.