改进IVIF-BWM的新高考数学试题综合难度模型的构建与应用-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Construction and Application of Comprehensive Difficulty Model for New College Entrance Examination Mathematics Questions Based on Improved IVIF-BWM

作者:: 陈艳玲1; 谢加良1; 2; 刘小辉1; 3; 1.集美大学理学院，福建厦门 361021；2.数字福建大数据建模与智能计算研究所，福建厦门 361021；3.厦门大学教育研究院，福建厦门 361005

Author(s):: CHEN Yanling1; XIE Jialiang1; 2; LIU Xiaohui1; 3; 1.School of Science,Jimei University,Xiamen 361021,China;2.Institute of Big Data Modeling and Intelligent Computing,Digital Fujian,Xiamen 361021,China;3.Institute of Education,Xiamen University,Xiamen 361005,China

Keywords:: interval value intuitionistic fuzzy; best worst method; new college entrance examination; mathematics questions; comprehensive difficulty model

摘要:: 以《中国高考评价体系》为蓝本，根据新高考数学试题的特点，构建新高考数学试题难度指标模型。针对现有区间值直觉模糊最优最劣方法（interval value intuitionistic fuzzy best worst method,IVIF-BWM）的不足，提出了改进的IVIF-BWM。该方法建立了基于乘法一致的区间值直觉模糊偏好关系（interval value intuitionistic fuzzy preference relation,IVIFPR）的目标规划模型求解准则的最优区间值直觉模糊（interval value intuitionistic fuzzy,IVIF）权重，并推导出IVIF环境下的一致性指标（consistency index,CI）和一致性比率（consistency ratio,CR）来验证结果的可靠性，将改进的IVIF-BWM用于计算难度指标和难度水平的权重，建立新高考试题综合难度模型。最后利用该模型评价2022年新高考数学试卷，验证所构建的新高考数学试题综合难度模型的有效性。

Abstract:: Firstly,using the China College Entrance Examination Evaluation System as the method guide and according to the examination characteristics of the new college entrance examination mathematics questions,this paper constructed a comprehensive difficulty index model of mathematics in the new college entrance examination.Then,according to the shortcomings of the existing interval value intuitionistic fuzzy best worst method(IVIF-BWM),this paper developed an improved IVIF-BWM that establishes a goal programming model based on the multiplicative consistent interval value intuitionistic fuzzy preference relation(IVIFPR) to derive the optimal interval value intuitionistic fuzzy(IVIF) weight of criteria,and then proposed the consistency index(CI) and consistency ratio(CR) under IVIF environment to verify the reliability of the derived results.The improved IVIF-BWM was used to calculate the weights of the difficulty indexes and the difficulty levels,so as to establish a comprehensive difficulty model for the new high exam questions.Finally,this model is used to analyze difficulty characteristics of the new college entrance exam mathematics paper in 2022,which verified the effectiveness of comprehensive difficulty model for new college entrance examination mathematics questions.