Research On Knowledge Structure Delineated By Fuzzy Skill Multimap

Knowledge space theory(KST)understands the knowledge level of learners in a certain field according to their answers to a series of questions at different levels.There are only two possibilities for the learner to answer questions that are completely correct and incorrect.In fact,differences in learners’ cognitive ability will affect learners’ answers to questions.Skills represent underlying cognitive abilities.In competency-based knowledge space theory(Cb-KST),learners’ knowledge is embodied in two different dimensions: the state of knowledge that learners can show,namely performance level;Learner’s potential competency state,namely competency level.In this paper,the relationship between the two-universe rough set model and Cb-KST is established,and the definition of the l-fringe of knowledge state is given.On this basis,we explore the method of constructing knowledge space and simple closure space by using the approximation operator of the two-universe rough set model respectively,and then describe the l-fringe of knowledge state of knowledge space,simple closure space and knowledge structure by using the approximation operator respectively.Furthermore,an algorithm is designed to reduce the skill set while keeping the knowledge structure unchanged,and an algorithm to guide the learner to the next step according to the l-fringe.Taking into account the effects of learners’ age and other factors,the acquisition of learners’ cognitive ability is a process of constant development from low level to high level towards maturity.From the perspective of competence level,fuzzy skill map or fuzzy skill multimap indicates that the answers to questions require different proficiency levels of skills.Based on fuzzy skill multimap,this paper analyzes and discusses the conditions in expression of fuzzy skill multimap to knowledge space,simple closure space and learning space.Then,we find the conditions which can represent the separability and separability of items in knowledge structure respectively in the expression of fuzzy skill multimap.Center on the distributed fuzzy skill multimap and the mesh of knowledge structures,this paper discusses the mutual consistency between the substructure and the parent knowledge structure about the separability(bi-separability)of items in knowledge structure.Stefanutti et al.proposed to replace skills with operations or operation chains(procedure),and described the process of problem solving as extracting an operation sequence from the set and applying the operation sequence to the initial state of things to obtain the final state of things.A method of deducing knowledge structure from problem space in an automatic way is proposed.In this paper,discriminative knowledge structure and bi-discriminative knowledge structure are introduced in the assessment of procedural knowledge.The theoretical conditions and the effective algorithms of deducing discriminative knowledge structure and bi-discriminative knowledge structure from problem space through skill map are discussed respectively.