多分知识结构析取模型及其应用  

The Disjunctive Model of Polytomous Knowledge Structure and Its Application

作　　者：林英茹 李进金 李长清 黄宝坤 LIN Yingru;LI Jinjin;LI Changqing;HUANG Baokun(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《山西大学学报(自然科学版)》2025年第1期192-202,共11页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11871259,12271191);福建省自然科学基金(2024J01803,2020J02043,2022J01912,2022J01306,2022J05169)。

摘　　要：合取属性映射的定义首次以公理化的形式给出,由此产生了多分知识结构合取模型理论。本文提出了析取属性映射的公理化定义,并考虑了析取相容性和析取完备性的条件,研究其与多分知识状态、属性结构和多分知识结构的关系,通过属性映射和项目响应函数建立可用属性和可观察项目响应之间的确定性关系。得到了多分知识结构的充要条件是属性映射析取相容且完备于属性结构,从而建立由析取属性映射诱导的多分知识结构的理论。所提出的方法具有广泛适用性,能在教学模式、教育评价、教育心理等场景中处理可能遇到的大量析取规则下的多分项目。The definition of conjunctive attribute mapping was first presented in an axiomatic form,which gave rise to the conjunctive model theory of polytomous knowledge structures.This paper presents an axiomatic definition of disjunctive attribute mapping.Considering the conditions of disjunctive compatibility and completeness,we study their relationships with polytomous knowledge state,attribute structure,and polytomous knowledge structure,and establish a deterministic relationship between available attributes and observable project responses through attribute mapping and project response function.The necessary and sufficient condition for polytomous knowledge structure is that the attribute mapping is disjunctively consistent and complete with respect to the attribute structure,thus establishing the theory of polytomous knowledge structure induced by the disjunctive attribute mapping.The proposed method has wide applicability and can handle a large number of disjunctive rules under polytomous projects in scenarios such as teaching models,educational evaluation,and educational psychology.

关 键 词：析取属性映射 析取相容性 析取完备性 多分知识状态 多分知识结构 

分 类 号：O189.1[理学—数学]