Fermatean fuzzy set, a significant extension of intuitionistic fuzzy set offer enhanced flexibility to address imprecise information than intuitionistic fuzzy set. In this, study, the parameters of the transportation problem are considered as Fermatean fuzzy numbers and aim to develop a solution framework based on this advanced fuzzy set theory. In order to do this, firstly a ranking function for Fermatean fuzzy number is proposed based on the concept of information reliability. Secondly, three types of transportation problems are considered in which the parameters are Fermatean fuzzy numbers. Moreover, the parameters of the transportation problem are converted in to their equivalent crisp values using the proposed ranking function and then solved by the standard algorithmic approaches using LINGO software. Finally, the significant of the proposed ranking function is discussed and validated through the results of the provided numerical examples.