A New Approach to Multiple Criteria Decision-Making Using the Dice Similarity Measure under Fermatean Fuzzy Environments

Many contemporary multiple criteria decision-making (MCDM) problems are rather complicated and uncertain to manage. MCDM problems can be complex because they involve making decisions based on multiple conflicting criteria, and they can be uncertain because they often involve incomplete or subjective information. This can make it difficult to determine the optimal solution to the problem. Over the last decades, tens of thousands MCDM methods have been proposed based on fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). In this paper, we propose a new MCDM method based on Fermatean fuzzy sets (FFSs) and improved Dice similarity measure (DSM) and generalized Dice similarity measures (GDSM) between two FFSs with completely unknown weights of criteria. When a decision matrix is given, we calculate the weights of criteria using a normalized entropy measure while the weights of criteria are not given by the decision-maker. Then, we use the proposed improved DSM and GDSM between two FFSs that take the hesitancy degree of elements of FFSs into account and develop a new MCDM method. Finally, we use the values of the proposed improved DSM and GDSM between two FFSs to get the preference order of the alternatives. The proposed method can overcome the drawbacks and limitations of some existing methods that they cannot get the preference order of the alternatives under Fermatean fuzzy (FF) environments.