Vague集相似度量模型的研究  

A New Similarity Measure Model between Vague Sets

作　　者：彭祖明[1] 陈义华[2] 

机构地区：[1]长江师范学院数学与计算机学院,重庆408100 [2]重庆大学数理学院,重庆400044

出　　处：《重庆师范大学学报（自然科学版）》2013年第3期85-88,共4页Journal of Chongqing Normal University:Natural Science

基　　金：长江师范学院科研资助项目(No.2010C3JSK-1082)

摘　　要：鉴于Vague集的相似度量在模糊推理、模式识别、聚类分析、决策分析等领域的广泛运用,本文首先对已有Vague值的相似度量模型进行了分析,发现已有的模型在应用时所得的结果或者不符合人的直觉,或者明显违背客观实际,或者存在区分度不足。然后提出了一个新的Vague值相似度量模型m(x,y)=1/2+ψ(x,y)/2-S(x,y)/4-|tx-ty|/4,并证明了该模型满足文献[1-4]相似度量的公理化定义。在提出的Vague值相似度量模型的基础上,建立了Vague集的相似度量一个新模型M(A,B)=∑ni=1m(A(xi),B(xi()))/n。最后,通过数值实验,新模型度量结果又较好符合人的直觉以及具有较好的区分度。The similarity measurement between vague sets is widely applied in fuzzy reasoning, pattern recognition, cluster analysis, decision analysis, et al. This need that the similarity measure model between vague sets has a good degree of discrimination, and the measurement results can accord with the intuition of human being. Based on this requirement, first, some analyzing was carried out on existing similarity measure models of Vague sets, from analyzing we found that some model have the shortcoming on discrimina- tion, and some model＇s measurements can＇t accord with the intuition of human being, et al. Secondly, a new model （ M（A, B） ∑ni=1m（A（xi）,B（xi））/nof similarity measure between Vague sets was established. To illustrate the proposed model＇s merit, two experimentations were carried out. The experimental results show that the proposed model had good discrimination, and can o- vercome the shortcoming of existing model.

关 键 词：VAGUE集 相似度量 模型 直觉 

分 类 号：O159[理学—数学]