Since the intuitionistic fuzzy set (IFS) was proposed by Atanassov, many explorations of this particular fuzzy set were conducted. One of the most important areas is the study of similarity and distance between IFSs, which can measure the degree of deviation of objects with uncertain and vague features, and this technique has great value and potential to solve the fuzzy and uncertain problems in the real world. Based on our previous similarity/distance measure model DJJ (α, β), a new method is proposed for improving the performance of similarity/distance measure model of IFSs, which is derived from the sum of the areas of two triangles constructed by the transformed isosceles triangles of two IFSs. A great effort is made to prove the validity of the proposed method by mathematical derivation. In order to further demonstrate the performance of the proposed method, we apply this method to solve some practical problems such as pattern recognition, medical diagnosis, and cluster analysis. In addition, we also list a series of the existing methods which are used to compare with the proposed method to prove the effectiveness and superiority. The experimental results confirm that the performance of the proposed method exceeds most of the existing methods.

中文翻译：

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基于变换等腰直角三角形面积的直觉模糊集之间的有效相似/距离度量及其应用

由于直觉模糊集（IFS）由Atanassov提出，因此对该特定模糊集进行了许多探索。最重要的领域之一是研究IFS之间的相似性和距离，它可以测量具有不确定和模糊特征的对象的偏离程度，并且该技术对于解决现实世界中的模糊和不确定性问题具有巨大的价值和潜力。 。在我们之前的相似度/距离度量模型DJJ（α，β）的基础上，提出了一种新的方法来提高IFS的相似度/距离度量模型的性能，该方法是通过将变换后的两个三角形的面积之和得出两个IFS的等腰三角形。为了通过数学推导证明所提出的方法的有效性，人们付出了巨大的努力。为了进一步证明该方法的性能，我们将该方法用于解决一些实际问题，例如模式识别，医学诊断和聚类分析。此外，我们还列出了一系列现有方法，用于与提出的方法进行比较，以证明其有效性和优越性。实验结果证实了该方法的性能超过了大多数现有方法。