Two Variable Precision Model For Constructing Knowledge Structure

Knowledge space theory,as an assessment system,has become a powerful tool for adaptive evaluation and learning assistance.In order to broaden the application scope of knowledge space theory,many scholars have carried out a series of studies in combination with other fields,such as formal concept analysis,rough set theory,item response theory,etc.The combination of different fields can deal with different problems,including but not limited to the construction of knowledge structure,skill reduction,skill evaluation,problem screening.Competency-based methods for fast and accurate construction of individual knowledge structures are studied.It can not only relate problems to the skills that individuals have mastered,but also explain the fact that individuals have different knowledge structures behind solving the same problems.Therefore,this paper attempts to combine skill map and skill function with inclusion degree to discuss the construction of delineated knowledge structure models and the choice of learning path of individual.It plays an important role in enriching the content and application of knowledge space theory.The research of this paper mainly includes the following innovative work:First,by combining the inclusion degree with a skill map and a skill function,the concepts of skill inclusion degree and competency inclusion degree are proposed and their properties are discussed.Next,based on the disjunctive,conjunctive,and competency models proposed by Doignon,we consider the problem that the conditions for delineating knowledge structure are too loose and harsh.On the basis of skill inclusion degree and competency inclusion degree,the variable precision α-model and variable precisionα-competency model of delineated knowledge structure are constructed,and their relation with the model of Doignon and the relationship between knowledge structures are discussed.Then,well-graded knowledge structures have good properties.The conditions that a skill map to delineates well-graded knowledge structures are taken into account based on the skill inclusion degrees.Finally,to eliminate redundant skill subsets,the concepts of equivalent skill subsets and minimal skill subsets are proposed by using the idea of rough set attribute reduction.We then present the method that preserves knowledge structure invariance and demonstrate its effectiveness with experiments on real data.