This paper presents a new Multi-criteria Decision-Making (MCDM) method with Fermatean fuzzy sets (FFSs). The proposed method uses the entropy theory to determine the weights of criteria and utilize cosine similarity measures to determine the best alternative. First, we develop a new Fermatean fuzzy entropy formula based on the Euclidean distance between Fermatean fuzzy number (FFN) and its compliment. The properties of the proposed formula and the proof of the properties are also given. Then, Fermatean fuzzy cosine similarity measures are introduced. We develop four different Fermatean fuzzy cosine similarity measures, also properties and proof of the properties are worked out systematically. Then, the algorithm of the proposed Fermatean fuzzy MCDM method, which includes Fermatean fuzzy entropy and Fermatean fuzzy cosine similarity measures, is introduced. The advantage of the proposed method is that Fermatean fuzzy entropy calculates how much valuable knowledge the current data provides in weights of criteria, and Fermatean fuzzy cosine similarity measures define the similarity between alternatives and ideal solution and negative ideal solution, in this way the method determines the best alternative smoothly. To show the applicability of the proposed method, an illustrative example is given for third party logistic (3PL) firm evaluation problem in cold chain management. In the illustrative example section, we determine six different criteria and six different 3PL alternatives. Then, alternatives are evaluated according to the proposed Fermatean fuzzy MCDM method. Moreover, the results are compared to the Euclidean measure, and sensitivity analysis is also performed. The comparison analysis results show that our model works efficiently and effectively.

中文翻译：

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基于新费马模糊理论的模糊MCDM方法

本文提出了一种新的带有费马模糊集 (FFS) 的多准则决策 (MCDM) 方法。所提出的方法使用熵理论来确定标准的权重，并利用余弦相似性度量来确定最佳替代方案。首先，我们基于费马模糊数（FFN）与其补码之间的欧几里德距离，开发了一个新的费马模糊熵公式。还给出了所提出公式的性质和性质的证明。然后，引入了费马模糊余弦相似度度量。我们开发了四种不同的费马模糊余弦相似度度量，并且系统地制定了性质和性质的证明。然后，提出的 Fermatean 模糊 MCDM 方法的算法，包括 Fermatean 模糊熵和 Fermatean 模糊余弦相似度度量，介绍。该方法的优点是费马模糊熵计算了当前数据在准则权重中提供了多少有价值的知识，而费马模糊余弦相似度度量定义了备选方案与理想解和负理想解之间的相似性，通过这种方式，该方法确定顺利的最佳选择。为了展示所提出方法的适用性，给出了冷链管理中第三方物流（3PL）公司评估问题的说明性示例。在说明性示例部分，我们确定了六种不同的标准和六种不同的 3PL 备选方案。然后，根据提出的 Fermatean 模糊 MCDM 方法评估备选方案。此外，将结果与欧几里得度量进行了比较，并进行了敏感性分析。