1. College of Command and Control Engineering, Army Engineering University of PLA, Nanjing 210007; 2. Anhui Province Key Laboratory of Big Data Analysis and Application, School of Computer Science and Technology, University of Science and Technology of China, Hefei 230027
Abstract：The relevance between knowledge in the instructional scenarios draws much attention. The existing research usually focuses on modeling the relationship between two knowledge points. However, the complex relevance in knowledge sets is ignored, which results in the deviation of the research results. Aiming at this problem, the fuzzy measure is introduced to quantify the knowledge set, and then a modeling method of knowledge relevance based on fuzzy measures is proposed. Firstly, three different knowledge relationships are analyzed grounded on the cognitive theory, and the knowledge relevance is modeled with fuzzy measures. Then, the practicability of the modeling method is demonstrated by the practical scenario. Secondly, based on fuzzy measure modeling, the importance and interaction of knowledge are discussed from the perspective of knowledge relevance. Finally, the application of knowledge relevance in cognitive diagnosis is studied. The influence of knowledge relevance on cognitive diagnosis is demonstrated through the experiments on real-world datasets. The results show that the proposed method predicts precisely with better interpretability.
[1] SLAVIN R E.Educational Psychology: Theory and Practice. 7th Edition. London, UK: Pearson, 2002. [2] 钟卓,唐烨伟,钟绍春,等.人工智能支持下教育知识图谱模型构建研究.电化教育研究, 2020, 41(4): 62-70. (ZHONG Z, TANG Y W, ZHONG S C, et al. Research on Constructing Model of Educational Knowledge Map Supported by Artificial Intelligence. E-Education Research, 2020, 41(4): 62-70.) [3] PIAGET J, BROWN T, THAMPY K J.The Equilibration of Cognitive Structures: The Central Problem of Intellectual Development. Chicago, USA: University of Chicago Press, 1985. [4] 徐显龙,周知恂,嵇云,等.基于4C/ID模型的复杂技能综合学习设计及成效.中国电化教育, 2019(10): 124-131. (XU X L, ZHOU Z X, JI Y, et al. Design and Effectiveness of Comprehensive Learning for Complex Skills Based on 4C/ID Model. China Educational Technology, 2019(10): 124-131.) [5] THORNDIKE E L, WOODWORTH R S.The Influence of Improvement in One Mental Function upon the Efficiency of Other Functions(I). Psychological Review, 1901, 8(3): 247-261. [6] MAYER R.Applying the Science of Learning. London, UK: Pearson, 2010. [7] GUO L, BAO Y, WANG Z R, et al. Cognitive Diagnostic Assessment with Different Weight for Attribute: Based on the Dina Model. Psychological Reports, 2014, 114(3): 802-822. [8] 罗照盛. 认知诊断评价理论基础.北京:北京师范大学出版社, 2019. (LUO Z S.Fundamentals of Cognitive Diagnostic Assessment. Beijing, China: Beijing Normal University Press, 2019.) [9] MENG L L, ZHANG M X, ZHANG W X, et al. CS-BKT: Introducing Item Relationship to the Bayesian Knowledge Tracing Model. Interactive Learning Environments, 2019, 29(8): 1393-1403. [10] CARMONA C, MILLÁN E, PÉREZ-DE-LA-CRUZ J L, et al. Introducing Prerequisite Relations in a Multi-layered Bayesian Stu-dent Model//Proc of the International Conference on User Mode-ling. Berlin, Germany: Springer, 2005: 347-356. [11] LEIGHTON J P, GIERL M J, HUNKA S M.The Attribute Hierarchy Method for Cognitive Assessment: A Variation on Tatsuoka's Rule-Space Approach. Journal of Educational Measurement, 2004, 41(3): 205-237. [12] WANG C J, GIERL M J.Using the Attribute Hierarchy Method to Make Diagnostic Inferences about Examinees' Cognitive Skills in Critical Reading. Journal of Educational Measurement, 2011, 48(2): 165-187. [13] CHEN P H, LU Y, ZHENG V W, et al. Prerequisite-Driven Deep Knowledge Tracing//Proc of the IEEE International Conference on Data Mining. Washington, USA: IEEE, 2018: 39-48. [14] LIANG C, YE J B, WU Z H, et al. Recovering Concept Prerequisite Relations from University Course Dependencies//Proc of the 31st AAAI Conference on Artificial Intelligence. Palo Alto, USA: AAAI, 2017: 4786-4791. [15] ROY S, MADHYASTHA M, LAWRENCE S, et al. Inferring Concept Prerequisite Relations from Online Educational Resources//Proc of the 31st AAAI Conference on Innovative Applications of Artificial Intelligence. Palo Alto, USA: AAAI, 2019: 9589-9594. [16] YANG Y M, LIU H X, CARBONELL J, et al. Concept Graph Learning from Educational Data//Proc of the 8th ACM International Conference on Web Search and Data Mining. New York, USA: ACM, 2015: 159-168. [17] GAO W B, LIU Q, HUANG Z Y, et al. RCD: Relation Map Driven Cognitive Diagnosis for Intelligent Education Systems//Proc of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval. New York, USA: ACM, 2021: 501-510. [18] 张暖,江波.学习者知识追踪研究进展综述.计算机科学, 2021, 48(4): 213-222. (ZHANG N, JIANG B.Review Progress of Learner Knowledge Tracing. Computer Science, 2021, 48(4): 213-222.) [19] TONG S W, LIU Q, HUANG W, et al. Structure-Based Know-ledge Tracing: An Influence Propagation View//Proc of the IEEE International Conference on Data Mining. Washington, USA: IEEE, 2020: 541-550. [20] MA W C.A Diagnostic Tree Model for Polytomous Responses with Multiple Strategies. British Journal of Mathematical and Statistical Psychology, 2019, 72(1): 61-82. [21] DE LA TORRE J, DOUGLAS J A. Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data. Psychometrika, 2008, 73(4): 595-624. [22] MA W C, GUO W J.Cognitive Diagnosis Models for Multiple Strategies. British Journal of Mathematical and Statistical Psycho-logy, 2019, 72(2): 370-392. [23] SUGENO M.Theory of Fuzzy Integrals and Its Applications. Ph.D. Dissertation. Tokyo, Japan: Tokyo Institute of Technology, 1974. [24] BELIAKOV G, DIVAKOV D.On Representation of Fuzzy Mea-sures for Learning Choquet and Sugeno Integrals. Knowledge-Based Systems, 2020, 189. DOI: 10.1016/j.knosys.2019.105134. [25] TORRA V, NARUKAWA Y.The Interpretation of Fuzzy Integrals and Their Application to Fuzzy Systems. International Journal of Approximate Reasoning, 2006, 41(1): 43-58. [26] 余晓晗,徐泽水,刘守生,等.复合打击下的火力分配方案评估.系统工程与电子技术, 2014, 36(1): 84-89. (YU X H, XU Z S, LIU S S, et al. Evaluations of Fire Assignment Alternatives in the Situation of Composite Strikes. System Engineering and Electronics, 2014, 36(1): 84-89.) [27] BELIAKOV G, PRADERA A, CALVO T.Aggregation Functions: A Guide for Practitioners. Berlin, Germany: Springer, 2007. [28] ISLAM M A, ANDERSON D T, PINAR A J, et al. Data-Driven Compression and Efficient Learning of the Choquet Integral. IEEE Transactions on Fuzzy Systems, 2017, 26(4): 1908-1922. [29] JAVIER M, SERGE G, PILAR B.k-Maxitive Fuzzy Measures: A Scalable Approach to Model Interactions. Fuzzy Sets and Systems, 2017, 324: 33-48. [30] MURRAY B, ISLAM M A, PINAR A J, et al. Explainable AI for Understanding Decisions and Data-Driven Optimization of the Choquet Integral//Proc of the IEEE International Conference on Fuzzy Systems. Washington, USA: IEEE, 2018. DOI: 10.1109/FUZZ-IEEE.2018.8491501. [31] MUROFUSHI T, SONEDA S.Techniques for Reading Fuzzy Mea-sures(III): Interaction Index//Proc of the 9th Fuzzy System Symposium. Tokyo, Japan: JST, 1993: 693-696. [32] GIERL M J.Making Diagnostic Inferences About Cognitive Attri-butes Using the Rule-Space Model and Attribute Hierarchy Method. Journal of Educational Measurement, 2007, 44(4): 325-340. [33] 刘淇,陈恩红,朱天宇,等.面向在线智慧学习的教育数据挖掘技术研究.模式识别与人工智能, 2018, 33(1): 77-90. (LIU Q, CHEN E H, ZHU T Y, et al. Research on Educational Data Mining for Online Intelligent Learning. Pattern Recognition and Artificial Intelligence, 2018, 33(1): 77-90.) [34] PARDOS Z A, HEFFERNAN N T, RUIZ C, et al. The Composition Effect: Conjunctive or Compensatory? An Analysis of Multi-skill Math Questions in ITS//Proc of the 1st International Conference on Educational Data Mining. Berlin, Germany: Springer, 2008: 147-156. [35] GRABISCH M, MUROFUSHI T, SUGENO M.Fuzzy Measures and Integrals: Theory and Applications. Berlin, Germany: Sprin-ger, 2000. [36] WU R Z, LIU Q, LIU Y P, et al. Cognitive Modelling for Predicting Examinee Performance[C/OL]. [2021-09-14]. http://staff.ustc.edu.cn/~cheneh/paper_pdf/2015/Runze-Wu-IJCAI.pdf. [37] LIU Q, WU R Z, CHEN E H, et al. Fuzzy Cognitive Diagnosis for Modelling Examinee Performance. ACM Transactions on Intelligent Systems and Technology, 2018, 9(4): 1-26. [38] ISLAM M A, ANDERSON D T, PINAR A J, et al. Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks. IEEE Transactions on Fuzzy Systems, 2020, 28(7): 1291-1300. [39] DRASGOW F, HULIN C L.Item Response Theory//DUNNETTE M D, HOUGH L M, eds. Handbook of Industrial and Organizational Psychology. Palo Alto, USA: Consulting Psychologists Press, 1990: 577-636. [40] DECARLO L T.On the Analysis of Fraction Subtraction Data: The DINA Model, Classification, Latent Class Sizes, and the Q-Matrix. Applied Psychological Measurement, 2011, 35(1): 8-26. [41] GRABISCH M.The Representation of Importance and Interaction of Features by Fuzzy Measures. Pattern Recognition Letters, 1996, 17(6): 567-575.
2022, Vol. 35 
