一种新的直觉模糊相似度及在模式识别上的应用

A Novel Similarity Measure between Intuitionisitc Fuzzy Sets with Application to Pattern Recognition

直觉模糊集是模糊理论的一个经典模型,被广泛地应用于处理模糊和不确定问题。相似度是直觉模糊集上的一种重要的不确定性度量。现有的相似度计算方法并未充分考虑犹豫度所表示的实践语义且常常出现违反直觉的问题。通过考虑隶属度、非隶属度、以及犹豫度所表达的模糊语义,本文修改了直觉模糊相似度的定义,提出了一种新的直觉模糊相似度的计算方法,分析了该方法的性质,证明了该方法满足直觉模糊相似度的定义。通过数值实验,验证了该方法的有效性。最后,将所提出的相似性度应用于模式识别问题。实验结果表明,所提出的方法可以避免现有方法的缺点,是一种准确、优越的方法。

Intuitionistic fuzzy set is a classical model of fuzzy theory,and it is widely used to deal with fuzzy and uncertain problems in many practical applications.Similarity measure is an important uncertainty measurement in intuitionistic fuzzy sets theory.Without fully considering the practical semantics of hesitation degree,the existing intuitionistic fuzzy similarity measures have the problem of counterintuitive results in some cases.In this paper,by considering the fuzzy semantics expressed by membership degree,non-membership degree and hesitation degree,a novel similarity measure between intuitionistic fuzzy sets is proposed,the properties of the proposed measure are analyzed,it is also proved that the measure satisfies the definition of the similarity measure for intuitionistic fuzzy sets.The numerical experiments are used to test the validity of the proposed measure.Finally,the proposed similarity measure is applied to deal with pattern recognition problems.The experimental results show that the proposed measure is an accurate and superior measure that can avoid the shortcomings of most existing measures.