Vague集的相似度理论

Theory of similarity measures between Vague sets

基于对现有Vague集(值)之间相似度度量方法的分析,给出了基本相似度和强相似度的定义,引入了能反映相似度与距离内在联系的边界条件,减少了相似度选取与构造的盲目性与随意性。基于Hausdorff距离给出了一种相似度度量新方法,并将该方法应用于离散论域及连续论域,得到了若干对应的加权相似度的计算公式。为解决基于Vague集的模式匹配和决策分析等问题作了理论上的准备,也为吸收和利用Fuzzy集、Rough集理论的相关结果和思想提供了方便。

The normal definition of the similarity degree between Vague sets（or elements） is proposed based on some pres-ent methods.Moreovert,he boundary condition is worked out through the investigating on the differences and relationships be-tween the distance and the similarity,and an example concerned with the similarity between classical sets helps to clarify the boundary condition.Knowing the boundary conditiont,he blindness in constructing and choosing a proper similarity mea-sure is surely reduced.Finally,a new method based on Hausdorff distance is established,and the case of continuous or dis-crete universe of discourse is consideredr,espectively.