作　　者： ;

机构地区： 广东外语外贸大学

出　　处： 《南京大学学报：自然科学版》 2017年第3期462-475,共14页

摘　　要： 1986年Atanassov提出直觉模糊集后,提出了多种直觉模糊集的距离公式,然而鲜有分析各种距离公式之间的差异.基于此,提出一种基于直觉模糊集三维坐标下的空间变换模型（隶属度、非隶属度、犹豫度）,并证明了在坐标变换下,变换前后向量空间具备相同的代数性质和代数结构.在此基础上,构建了一系列新的直觉模糊集空间模型及其上的距离.尤其重要的是,提出了两类带参数的距离公式,而且该两类距离公式的排序能力都随着参数的变化而变化,现有经典直觉模糊集距离公式都是新距离公式的特例.因此,将所有距离公式依据其排序能力分成两大类：强序距离和弱序距离.仿真实验结果表明,强序距离在聚类、分类和模式识别中的表现明显优于弱序距离,公开数据库的手写体图像识别实验也证明强序距离在模式识别中的优势. Since Atanassov introduced the concept of the intuitionistic fuzzy sets （IFS）in 1986, increasing distance measures between IFSs were presented by other researchers. However, few articles analyze the difference among these measuring distances. This paper first proposes a method based on the space transformation about all the three vectors（the membership, non-membership and hesitation degree）. Then it is shown that the transformed space has the same algebra structure and properties as the original. Considering this characteristic, we present a series of new spaces of the IFS and new measuring distances. Particularly,two sorts of special measuring distances with parameter are proposed and their ordering capability changes with their parameter values, and all of the classic measuring distances are their special cases. Therefore, all these measuring distances can be classified to be two classes according to their ordering capability： one is strong order distance, and the other weak order one. Results show that the strong order distance is superior to the weak one when applied to clustering, classification, and pattern recognition. The experiment of image recognition for handwritten words also proved the superiority of strong order distance in pattern recognition.

关 键 词： 直觉模糊集 软代数 强序距离 弱序距离 K-MEANS聚类算法 模式识别

分 类 号： [TP391]

领　　域： []