Modified methods to solve interval-valued Fermatean fuzzy multi-criteria decision-making problems

In a recently published paper, two methods were proposed to solve interval-valued Fermatean fuzzy multi-criteria decision-making problems (those in which the rating value of each alternative over each criterion is represented by an interval-valued Fermatean fuzzy number). In this paper, some numerical examples are considered to show that these existing methods fail to find the correct ranking of the alternatives. Also, the reasons for the failure of these existing methods are pointed out. Furthermore, new methods are proposed to solve the interval-valued Fermatean fuzzy multi-criteria decision-making problems by modifying existing methods. Moreover, the proposed modified methods are illustrated with the help of numerical examples. Finally, the ranking of the alternatives of the two existing real-life interval-valued Fermatean fuzzy multi-criteria decision-making problems is obtained by the proposed methods.