To date, for the purpose of solving the complex problems in the area of expert system, Multi criteria decision making is the best technique to offer the suitable solution. In the academic literature, the MCDM methods suffered from many challenges. The most important challenges are uncertainty and vagueness. One of the latest MCDM method, called the fuzzy decision by opinion score method (FDOSM). However, there are still some vagueness issues around these methods (mention some of them). According to the advantage of the Fermatean fuzzy set in solving these issues, in this research extends FDOSM into Fermatean-FDOSM so as to effectively benchmark the real-life problem. In this study, we present our methodology in two phases. The first phase presents the mathematical model of Fermatean-FDOSM which is composed of three stages of FDOSM. The second phase applied the new extension to benchmark the COVID-19 machine learning methods. The finding of Fermatean-FDOSM after comparing the result with the basic FDSOM and TOPSIS, is more logical and undergoing a systematic ranking. In the validation process, objective validation is applied to validate the final result of Fermatean-FDOSM. The result of Fermatean-FDOSM is valid, and more logical and in line with decision makers' opinions.