Extended group decision-making methods with 2-tuple linguistic Fermatean fuzzy sets

The primary objective of this research article is to present two novel tactical approaches, 2-tuple linguistic Fermatean fuzzy TOPSIS (2TLFF-TOPSIS) and 2-tuple linguistic Fermatean fuzzy ELECTRE I (2TLFF-ELECTRE I), for multi-attribute group decision-making based on 2-tuple linguistic Fermatean fuzzy data. The proposed algorithm exploits the benefits of novel 2-tuple linguistic Fermatean averaging operator to combine the insightful viewpoints of decision-making experts. The score function is used by the 2TLFF-TOPSIS to locate both positive and negative ideal solutions. The options are sorted based on the normalized Euclidean distance-based closeness index. Further, the proposed 2TLFF-ELECTRE I method devise the best option using the notions of 2TLFF concordance and 2TLFF discordance on the basis of score degrees. Finally outranking relations are achieved by the keen comparison of 2TLFF concordance and 2TLFF discordance indices with concordance and discordance levels. To assign the ranks of the alternatives, an outranking graph is then created. Also, we use visual representations to illustrate each stage of the suggested techniques. We provide two numerical examples related to site selection for installation of solar photovoltaic (PV) project and evaluation of financial management performance to illustrate the practicality and application of the proposed methodologies. To demonstrate the superiority and efficacy of the suggested methods, we perform comparative analysis.