图片模糊集的一种相似度量及其在模式识别中的应用

Similarity Measure Between Picture Fuzzy Sets and Its Application in Pattern Recognition

图片模糊集能刻画具有模糊性、不确定性和不一致性的信息,相似度量是刻画两个对象的相似程度。文中研究图片模糊集的相似度量。考虑图片模糊集3个隶属度的信息差,基于指数函数构造出一种新的相似度量。文中提出的相似度量不仅满足相似度量的公理化定义,并且在实际应用中得到合理的计算结果。将相似度量应用到模式识别中,与现存的一些相似度量进行对比分析,结果表明所提出的相似度量不仅可以弥补一些现存相似度量的缺陷,还可以得到合理的计算结果。

Picture fuzzy sets can depict information with fuzziness,uncertainty,and inconsistency.Similarity measure is a measure of the degree of similarity between two objects.The similarity measure between picture fuzzy sets is studied in this paper.Considering the information difference of the three membership degrees of picture fuzzy sets,a new similarity measure is constructed based on exponential function.The similarity measure proposed in this paper not only satisfies the axiomatic definition of the similarity measure,but also yields reasonable computational results in practical applications.We apply the proposed similarity measure to pattern recognition,and compare it with some existing similarity measures in examples.The results show that the proposed similarity measure can not only overcome the shortcomings of some existing similarity measures,but also obtain reasonable calculation results.