基于算数平均值的直觉模糊集合的相似度

从几何的角度出发,依据犹豫度将直觉模糊数转化为一个等腰直角三角形,把2个直觉模糊数之间的相似度定义为对应的等腰直角三角形对应点距离的平均值.在此基础上,引入了2个直觉模糊集的相似度,证明了它们都满足相似性公理.通过数值实例与已有的直觉模糊集的相似度进行比较,结果表明该相似度具有一定的优越性.最后,给出了该相似度在模式识别中的应用实例.

Similarity measure of intuitionistic fuzzy sets based on the arithmetic mean

Based on the geometric point of view,the intuitionistic fuzzy number is transformed into an isosceles right triangle according to the degree of hesitation. The similarity degree between two intuitionistic fuzzy numbers is defined as the average of the corresponding distance of the corresponding isosceles right triangle. On this basis,the similarity degree of two intuitionistic fuzzy sets is introduced,which proves that they all satisfy the similarity axiom.This study uses some examples to show that the proposed similarity measure between AIFSs can overcome the defects of the existing similarity measures. Finally,it applies the proposed similarity measure between AIFSs to deal with pattern recognition problems.