The Fermatean fuzzy set (FFS) is an effective and robust technique for handling ambiguity, to deal with issues that can’t be resolved using the concepts of Intuitionistic fuzzy set and Pythagorean fuzzy set. Due to its essential uses and crucial significance in solving insoluble real-world problems in a variety of sectors, FFS has generated a maze of research since its inception. In this elaborative study, we establish a clear definition for the concept of similarity measures along with their essential qualities in the context of FFS. Additionally, we introduced a group decision-making algorithm grounded in the suggested similarity measures to tackle the issues. The attribute weights are determined by utilizing the newly introduced similarity measures as part of the process. The credibility of the algorithm is demonstrated through a case of dengue diseases and a comparison of its results with some of the existing studies.

费马泰模糊集（FFS）是一种有效且稳健的处理歧义的技术，用于处理使用直觉模糊集和毕达哥拉斯模糊集的概念无法解决的问题。由于 FFS 在解决各个领域无法解决的现实问题方面具有重要用途和至关重要的意义，自成立以来，FFS 已经引发了一系列的研究。在这项详尽的研究中，我们为相似性度量的概念及其在 FFS 背景下的基本品质建立了明确的定义。此外，我们引入了一种基于建议的相似性度量的群体决策算法来解决这些问题。属性权重是通过利用新引入的相似性度量作为过程的一部分来确定的。通过登革热病例及其结果与一些现有研究的比较证明了该算法的可信度。