摘要
云模型作为处理不确定性的有效工具,其相似性度量对于诸多应用意义重大。通过聚焦于梯形云,在结合正态云特征曲线的几何分布特点与Hellinger距离衡量概率分布相似性的优势后,提出了一种基于Hellinger距离的梯形云相似度计算方法。给出梯形云模型的定义,明确其期望区间值、熵和超熵等数字特征。利用Hellinger距离构造了2种梯形云概念间的距离和相似度,并对度量所满足的性质进行证明和分析。在此基础上,设计提出了2种相似度算法。通过数值仿真实验和时间序列分类实验对所提算法与现有相似度算法进行对比。结果显示,所提算法有较好的相似度区分能力且CPU时间代价较低。将提出的算法与机器学习算法相比较,实验显示,所提算法的分类准确率处于较高水平,在实际应用中能够展现出良好的可行性与有效性。
As an effective tool for handling uncertainty,the cloud model plays an important role in many applications,and its similarity measurement is of great significance.Focusing on trapezoidal clouds,this study proposes a similarity computation method based on the Hellinger distance by integrating the geometric characteristics of normal cloud membership curves with the advantages of Hellinger distance in quantifying the similarity of probability distributions.The definition of the trapezoidal cloud model is provided,along with explicit descriptions of its numerical characteristics,including the interval-valued expectation,entropy,and hyper-entropy.Two types of distances and similarity measures between trapezoidal cloud concepts are constructed using the Hellinger distance,and their mathematical properties are analyzed and proven.On this basis,two similarity algorithms are designed.Comparative evaluations with existing similarity algorithms are conducted through numerical simulations and time-series classification experiments.The results show that the proposed algorithms achieve better discriminative capability and lower computational cost(CPU time).Compared with typical machine learning algorithms,the proposed method also demonstrates relatively high classification accuracy,indicating good feasibility and effectiveness in real-world applications.
作者
许昌林
孔祥钰
沈菊红
XU Changlin;KONG Xiangyu;SHEN Juhong(School of Mathematics and Information Sciences,North Minzu University,Yinchuan 750021;Ningxia Key Laboratory of Intelligent Information and Big Data Processing,North Minzu University,Yinchuan 750021)
出处
《重庆邮电大学学报(自然科学版)》
北大核心
2025年第6期830-845,共16页
Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition)
基金
宁夏自然科学基金优秀青年项目(2023AAC05046)
国家自然科学基金项目(62066001)
宁夏高等教育一流学科建设基金项目(NXYLXK2017B09)。
