A new score function based Fermatean fuzzy transportation problem

Abstract

Today the supply, the demand and transportation costs in a transportation problem (TP) cannot be measured precisely due to the inconstant economic and environment conditions. The aim of this paper is to solve transportation problem where supply, demand and transportation costs are Fermatean fuzzy numbers (FFNs). In the existing literature, several methods have been proposed for solving transportation problems with fuzzy parameters (FPs) but in all the proposed methods the parameters relating to the transportation problems are either generalized fuzzy numbers or Pythagorean fuzzy numbers (PFNs). The concept of Fermatean fuzzy sets (FFSs) are very new and using Fermatean fuzzy sets one can handle uncertain information more easily in the process of decision making. Therefore, in this paper, first time we have solved transportation problem with Fermatean fuzzy parameters. For solving the transportation problem with Fermatean fuzzy parameters, we have proposed an algorithm and solved the same by existing method. Then using arithmetic operations of Fermatean fuzzy number the optimal value can be obtained. To illustrate the proposed method we have solved a numerical example and computed results are presented and compared with the existing literature. Finally, the significance of the paper and the scope of future study are mentioned.