{"title":"On delineating forward- and backward-graded knowledge structures from fuzzy skill maps","authors":"Bochi Xu , Jinjin Li , Wen Sun , Bo Wang","doi":"10.1016/j.jmp.2023.102819","DOIUrl":null,"url":null,"abstract":"<div><p>Forward-graded and backward-graded structures of knowledge are two important classes of knowledge structures. Spoto and Stefanutti (2020) establish necessary and sufficient conditions for skill maps to delineate these structures. We introduce fuzzy skills to describe varying levels of proficiency in skills and extend the theoretical results of Spoto and Stefanutti (2020) for delineating forward- and backward-graded knowledge structures using fuzzy skill maps. The paper establishes necessary and sufficient conditions for fuzzy skill maps to delineate a backward-graded simple closure space, a forward-graded knowledge space, and a forward-graded simple closure space. Furthermore, the competence-based local independence model (CBLIM) with fuzzy skills is introduced and its unidentifiability is discussed.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102819"},"PeriodicalIF":2.2000,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Psychology","FirstCategoryId":"102","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022249623000755","RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Forward-graded and backward-graded structures of knowledge are two important classes of knowledge structures. Spoto and Stefanutti (2020) establish necessary and sufficient conditions for skill maps to delineate these structures. We introduce fuzzy skills to describe varying levels of proficiency in skills and extend the theoretical results of Spoto and Stefanutti (2020) for delineating forward- and backward-graded knowledge structures using fuzzy skill maps. The paper establishes necessary and sufficient conditions for fuzzy skill maps to delineate a backward-graded simple closure space, a forward-graded knowledge space, and a forward-graded simple closure space. Furthermore, the competence-based local independence model (CBLIM) with fuzzy skills is introduced and its unidentifiability is discussed.
期刊介绍：
The Journal of Mathematical Psychology includes articles, monographs and reviews, notes and commentaries, and book reviews in all areas of mathematical psychology. Empirical and theoretical contributions are equally welcome.
Areas of special interest include, but are not limited to, fundamental measurement and psychological process models, such as those based upon neural network or information processing concepts. A partial listing of substantive areas covered include sensation and perception, psychophysics, learning and memory, problem solving, judgment and decision-making, and motivation.
The Journal of Mathematical Psychology is affiliated with the Society for Mathematical Psychology.
Research Areas include:
• Models for sensation and perception, learning, memory and thinking
• Fundamental measurement and scaling
• Decision making
• Neural modeling and networks
• Psychophysics and signal detection
• Neuropsychological theories
• Psycholinguistics
• Motivational dynamics
• Animal behavior
• Psychometric theory
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