Uncorrected Author Proof Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-220707 IOS Press 1 A new extension of fuzzy decision by opinion score method based on Fermatean fuzzy: A benchmarking COVID-19 machine learning methods 1 2 3 4 Mahmood M. Salih a,∗ , Z.T. Al-Qaysi a , Moceheb Lazam Shuwandy a , M.A. Ahmed a , Kahlan F. Hasan b and Yousif Raad Muhsen c 5 6 a Computer Science Department, College of Computer Science and Mathematics, Tikrit University (TU), Tikrit, Iraq 7 8 b Informatics institute, Istanbul Technical University, Istanbul, Turkey 9 c Computer Science Department, College of Computer Science and Information Technology, University of Wasit, Wasit, Iraq 10 11 Abstract. 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. 12 13 14 15 16 17 18 19 20 21 22 Keywords: Fuzzy decision by opinion score method (FDOSM), machine learning, Fermatean fuzzy, COVID-19, multi-criteria decision-making 23 24 1. Introduction 25 Fundamentally, MCDM is a Decision making is 26 a reasoning approach of ordering available prefer- 27 ences so as to select the highly desirable. The decision 28 ∗ Corresponding author. Mahmood M. Salih, Computer Science Department, College of Computer Science and Mathematics, Tikrit University (TU), Tikrit, Iraq. Tel.: +964 770 184 9377; E-mail: mahmaher1989@gmail.com. making process aims to achieve the most desirable 29 objectives which have the least expected penalties 30 [1]. With the presence of uncertainty, insufficient 31 knowledge, and cases that involve multiple criteria 32 consideration, decision making often becomes more 33 complex. MCDM is the most popular branch of deci- 34 sion making [2]. MCDM refers to decision making 35 in the presence of multiple objectives or attributes[3]. 36 MCDM approach is often used with a view to 37 ISSN 1064-1246/$35.00 © 2022 – IOS Press. All rights reserved.