改进IVIF-BWM的新高考数学试题综合难度模型的构建与应用  

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

作　　者：陈艳玲 谢加良[1,2] 刘小辉 CHEN Yanling;XIE Jialiang;LIU Xiaohui(School of Science,Jimei University,Xiamen 361021,China;Institute of Big Data Modeling and Intelligent Computing,Digital Fujian,Xiamen 361021,China;Institute of Education,Xiamen University,Xiamen 361005,China)

机构地区：[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

出　　处：《集美大学学报(自然科学版)》2025年第1期76-87,共12页Journal of Jimei University:Natural Science

基　　金：教育部人文社会科学研究规划基金项目“应用型本科院校应用型理工科专业评价标准国际比较研究”(17YJA880070);福建省高等教育研究院重点课题“数字化转型下福建省高校人才培养现状及提升策略”(FGJ202403);福建省科技厅创新战略研究项目“‘福元宇宙’视域下公民数字素养影响因素与提升策略研究”(2023R0051)。

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。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.

关 键 词：区间值直觉模糊集 最优最劣方法 新高考 数学试题 综合难度模型 

分 类 号：O159[理学—数学] G633.6[理学—基础数学]