A Fuzzy MCDM Method Based on New Fermatean Fuzzy Theories

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.