Multi-criteria group decision making through full multiplicative form under hesitant Fermatean fuzzy environment

The main purpose of this research work is to develop a novel approach for multi-objective optimization within the framework of hesitant Fermatean fuzzy methodology incorporating both, the ratio analysis and the complete multiplicative form techniques, to effectively tackle multi-criteria group decision-making (MCGDM) challenges arising from uncertain and ambiguous data about weight values of the criteria set. We propose a novel distance measure while formulating the framework to quantify the distinction among hesitation Fermatean fuzziness after integrating Hausdorff metric and Hamming distance. Subsequently, the developed distance measure is used to determine the unspecified weights of criteria using the weight entropy approach. The same distance measure is utilized in the reference point technique to attain the inclination implications of potential choices or alternatives. While the global economy has been developed vigorously, a big amount of complex and uncertain data get involved in the evaluations and judgments of evaluators in MCGDM. Decision-makers may assign a set of preference values because of their diverse knowledge backgrounds and dissimilarity of benchmarks. Thus, it is very challenging for evaluators to impart their evaluations through Fermatean fuzzy elements. To overcome the existing limitations and drawbacks of classical MULTIMOORA technique have been overcome through an integrated strategy, specifically, by amalgamating hesitant Fermatean fuzzy-MULTIMOORA with quantitative strategic planning matrix. Moreover, a MCGDM algorithm has also been presented in the current research work. The practical applicability and viability of the suggested approach is demonstrated through its implementation in a real life scenario involving the ranking of strategies for a tile assembling organization. The suggested technique’s applicability and effectiveness, as well as the conclusions drawn using hesitant Fermatean fuzzy-MULTIMOORA, are distinguished from those derived using other existing method. These subsisting methodologies are examined not only from classical and fuzzy surroundings, but also in conjunction with certain other decision making approaches, including modified Pythagorean fuzzy-MOORA, considered as a special case of the created hesitant Fermatean fuzzy-MULTIMOORA framework.