一种基于模糊集理论的有效距离测度公式  

An Effective Distance Measurement Formula Based on Fuzzy Set Theory

作　　者：胡汭 王明刚[2] Hu Rui;WANG Minggang(College of Mathematics and Computer Science,Tongling University,Tongling 244000,Anhui;School of Mathematical Sciences,Nanjing Normal University,Nanjing 210024,China)

机构地区：[1]铜陵学院数学与计算机学院,安徽铜陵244000 [2]南京师范大学数学科学学院,南京210024

出　　处：《合肥学院学报（综合版）》2024年第2期22-27,共6页Journal of Hefei University：Comprehensive ED

基　　金：国家自然科学基金项目“重点行业碳中和技术创新与碳减排激励机制”(72243005);铜陵学院高校优秀青年骨干教师国内访学研修项目(gxgnfx2022068);铜陵学院校级质量工程项目“运筹学思政示范课程”(2023xj108)。

摘　　要：针对已有研究提出的多种距离测度公式在区分某些相近数据时的失效性,给出了一种优化后的距离测度公式,并证明该种优化后的距离测度公式不仅符合距离测度的三个基本性质即:非负性、三角不等式性和介质性;并通过计算比较分析,论证了该优化后的距离测度公式在处理某些特殊数据时的有效性和优越性,最后还通过实例分析论证了它在模式识别中的良好性能,为人们提取、分析处理数据以及进行人工智能相关的机器学习提供了良好的数学工具。Aiming at the failure of various distance measure formulas proposed in the existing research when distinguishing some similar data,an optimized distance measure formula is given,and it is proved that the optimized distance measure formula not only conforms to the three basic properties of distance measure:non-negativity,triangular inequality and medium.Through calculation and compar-ative analysis,the effectiveness and superiority of the optimized distance measure formula in dealing with some special data are demonstrated.Finally,its good performance in pattern recognition is dem-onstrated through case analysis,which provides a good mathematical tool for people to extract,analyze and process data and carry out machine learning related to artificial intelligence.

关 键 词：距离测度 VAGUE值 隶属度函数 模式识别. 

分 类 号：O159[理学—数学] TP301[理学—基础数学]