A note on knowledge structures delineated by fuzzy skill multimaps

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-01-16 DOI:10.1016/j.fss.2025.109282

Xiyan Cao , Fucai Lin , Wen Sun , Jinjin Li , Peijin Lin

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引用次数: 0

Abstract

Fuzzy skill multimaps can describe individuals' knowledge states from the perspective of latent cognitive abilities. A discriminative knowledge structure is reducing redundant items to vary the test with the aim of lightening the workload for students, and the bi-discriminative knowledge structure is useful for evaluating ‘relative independence’ items or knowledge points. Moreover, it is highly significant to determine the type of fuzzy skill multimap that delineates a discriminative or bi-discriminative knowledge structure. Additionally, we provide a characterization of fuzzy skill multimaps in order to delineate knowledge spaces, learning spaces and simple closure spaces respectively. Furthermore, there are some interesting applications in the meshing of the delineated knowledge structures and the distributed fuzzy skill multimaps. We also give a more precise analysis regarding the separability (resp. bi-separability) on which condition the information collected within a local assessment can reflect an assessment at the global level, and which condition any of the local domains can localize from given global assessment.

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模糊技能多图可以从潜在认知能力的角度描述个人的知识状态。判别型知识结构可以减少冗余项目，从而改变测试内容，达到减轻学生课业负担的目的；而双判别型知识结构则有助于评价 "相对独立 "的项目或知识点。此外，确定模糊技能多图的类型对划分判别式知识结构或双判别式知识结构意义重大。此外，我们还提供了模糊技能多映射的特征，以便分别划分知识空间、学习空间和简单闭合空间。此外，在划分的知识结构和分布式模糊技能多映射的网格中还有一些有趣的应用。我们还给出了更精确的可分性（或双可分性）分析，即在什么条件下，局部评估中收集的信息可以反映全局评估，以及在什么条件下，任何局部域都可以从给定的全局评估中定位。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.