Transportation problem in Fermatean fuzzy environment

Due to the uncertain economic and environmental situations of the society, it is impossible to quantify the supply, demand, and transportation costs of a transportation problem precisely. The purpose of this paper is to address the transportation problem where supply, demand, and transportation costs are Fermatean fuzzy numbers. Numerous approaches to addressing transportation problems with fuzzy parameters have been suggested in the literature to date, but in each of these approaches, the parameters corresponding to the transportation problems are either generalized fuzzy numbers or Pythagorean fuzzy numbers. With the help of Fermatean fuzzy sets (FFSs), a relatively new concept, one can manage ambiguous information more simply throughout the decision-making process. As a result, we have used Fermatean fuzzy parameters to solve the transportation problem in this research.  Here, we have developed an algorithm to solve the transportation problem with Fermatean fuzzy parameters and have also solved the problem using the existing method. Then, the optimal value can be obtained using arithmetic operations on Fermatean fuzzy numbers. We have solved a numerical example to demonstrate the proposed methodology, and the obtained results are presented and compared with the existing literature. The importance of the research and the scope of further research are then highlighted.