A Novel Approach to Solve the Interval-Valued Fermatean Fuzzy Transportation Problem

In any decision-making process, it is commonly observed that decision makers often face difficulty in specifying precise or crisp values for parameters due to doubts or hesitation. This uncertainty regarding the parameters leads to ambiguity in the decision-making process. To handle the uncertainty of transportation problem related parameters, numerous approaches have been proposed in the literature. However, in most of the approaches, the parameters pertinent to the problems are either fuzzy/intuitionistic fuzzy or pythagorean fuzzy numbers. A recent concept of an interval-valued fermatean fuzzy numbers provides a robust framework than existing fuzzy numbers for handling uncertain and incomplete data in practical applications. The aim of this paper is to introduce a novel formulation of the transportation problem by utilizing interval-valued triangular fermatean fuzzy numbers to represent transportation costs, as well as the values of supplies and demands. We propose a fermatean fuzzy programming approach to solve the transportation problem with interval-valued triangular fermatean fuzzy numbers. The proposed approach relies on the score function of interval-valued triangular fermatean fuzzy numbers and the order relation of interval numbers. To demonstrate the effectiveness of the proposed approach, we finally solve an illustrative application example.