ELECTRE is a family of multi-criteria decision analysis techniques, which has the ability to provide as much as possible precise and suitable set of actions or alternatives to the underlying problem by eliminating the alter-natives, which are outranked by others. Group decision-making is an effective process to provide the most appropriate solution to real-world decision-making scenarios by considering and merging the expert opinions of multiple individuals on the problem. The aim of this study is to present an extended version of the ELECTRE I model called the Fermatean fuzzy ELECTRE I method for of multi-criteria group decision-making with Fermatean fuzzy human assessments. The method proposed in this study has the possibility to solve multi-criteria group decision-making problems by using the Fermatean fuzzy decision matrix obtained in Fermatean fuzzy number form in the evaluations made with the available alternatives based on expert opinions. First, the mathematical description of the multi-criteria group decision-making problem with Fermatean fuzzy information has been given. Then, the proposed Fermatean fuzzy ELECTRE I method to deal with the problem has been presented. After the determination of the relative importance degree of experts, the Fermatean fuzzy aggregated averaging operator is employed to merge the individual Fermatean fuzzy decision matrices produced by the experts into the aggregated Fermatean fuzzy decision matrix. Next, for pairwise comparison of available alternatives with respect to considered criteria, the concepts of Fermatean fuzzy strong, midrange, and weak concordance and discordance sets are based on the approach of score function and accuracy function defined for Fermatean fuzzy numbers. Afterward, Fermatean fuzzy concordance and discordance matrices are defined, constructed by concordance and discordance indices. Finally, Fermatean fuzzy effective concordance and discordance matrices are computed to obtain Fermatean fuzzy aggregated outranking matrix, indicating abstract information on dominations of suit-able alternatives to the others. The proposed method will be used in material selection in distinct imple-mentations, exclusively in biomedical applications where the prosthesis materials should have similar characteristics to human tissues. Since biomedical materials are used in various parts of the human body for many different purposes, in this study, material selection will be made using the method presented for the femoral component of the hip joint prosthesis for orthopedists and practitioners who will choose biomaterials.