一种基于包含关系的Vague集新相似度量方法  

A New Similarity Measure Method for Vague Sets Based on Inclusion Relation

作　　者：冯卫兵[1] 韩玉 FENG Weibing;HAN Yu(School of Science,Xi′an University of Science&Technology,Xi′an 710054,China)

机构地区：[1]西安科技大学理学院,陕西西安710054

出　　处：《河南科技大学学报（自然科学版）》2023年第1期90-97,M0007,M0008,共10页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(71473194);陕西省技术创新引导专项(基金)项目(2020CGXNG-013)。

摘　　要：针对已有相似度量方法考虑因素不全面的情况,本文从二次投票出发同时考虑了二次投票中支持度、反对度和未知度的包含关系,合理设置系数,提出一种新的基于包含关系的Vague集相似度量方法,理论证明新相似度量方法满足相似度量的基本准则。分别选取小样本和大样本与已有相似度量方法进行比较,提出了一种新的相似度区分能力的定义。实验结果表明:对于小样本数据,本文提出的相似度量方法区分能力最大为0.14;对于大样本数据,本文提出的相似度量方法区分能力最大为119.8。将新相似度量方法分别应用于故障诊断、模式识别和多准则决策中,结果表明新的相似度量方法能够有效和合理地区分数据。In view of the fact that the factors considered in the existing similarity measure method are not comprehensive,this paper embarked from the second vote at the same time considering the inclusion relation of support,opposition and unknown degrees in the second vote and setting the coefficient reasonably.Thus,a new similarity measure method of Vague sets based on inclusion relation was proposed and the new similarity measure method met the basic criteria of similarity measure was proved by theory.A new definition of similarity discrimination ability was proposed by comparing the existing similarity measure methods with small sample and large sample respectively. Experimental results show that for small sample data, the maximum discrimination ability of the similarity measure method proposed in this paper is 0.14.For large sample data,the similarity measure method proposed in this paper has a maximum discrimination ability of 119. 8. The new similarity measure method is applied to fault diagnosis,pattern recognition and multi-criteria decision making respectively, which show that the new similarity measure method can distinguish data effectively and reasonably.

关 键 词：VAGUE集 相似度 包含关系 模式识别 多准则决策 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]