Multi-criteria group decision-making based on an integrated PROMETHEE approach with 2-tuple linguistic Fermatean fuzzy sets

The preference ranking organization method for enrichment evaluation (PROMETHEE) technique is a comprehensive and efficient multi-criteria decision-making (MCDM) method. This research study is devoted to establishing an improved version of the PROMETHEE approach based on 2-tuple linguistic Fermatean fuzzy sets (2TLFFS) to address the MCDM problems when decision-makers use linguistic variables to convey their judgments about alternatives. The membership and non-membership functions of 2TLFFS are used to evaluate the weight of each criterion and the evaluation of each alternative for each criterion. We propose a new pairwise deviation formula using the score function, which is then employed to develop preference functions. To get the preferences for the alternatives, we take Gaussian and usual preference functions and use them to create a preference index matrix. The PROMETHEE I method is used to determine the partial order of alternatives by evaluating the positive outranking flow and negative outranking flow of alternatives. Furthermore, the PROMETHEE II approach obtains the total ranking of the alternatives by calculating the net outranking flow. Moreover, a flowchart is used to demonstrate the method proposed by the 2TLFF-PROMETHEE. Using a numerical example, specifically the choice of an appropriate bank manager, we establish the practical implications and realism of the proposed method. The results of the proposed work are then compared with those of the existing approach to more accurately reflect the capacity and effectiveness of the proposed work. Finally, we conclude that the 2TLFF-PROMETHEE technique established within a 2TFFS framework is highly effective and reliable in addressing MCGDM issues.