This article, in order to address impreciseness, initiated the notion of dual hesitant fermatean fuzzy sets (DHFFSs), as a generalization of the combination of dual hesitant fuzzy set (DHFS), dual hesitant Pythagorean fuzzy set (DHPFS) and Fermatean fuzzy set (FFS). The authors defined the fundamental set of operations for DHFFS. Additionally, the authors have also proposed two ranking functions and an accuracy function for the ordering of this novel set. In order to facilitate the pragmatic implementation of DHFFS in optimization, the authors formulated three types of transportation problem with dual hesitant Fermatean fuzzy (DHFF) parameters. To optimize the DHFF-TP, an algorithm was proposed with the help of one of the proposed ranking functions. Artificial neural network is also applied to the transportation problems in DHFF environment. A numerical example based on the transportation of COVID-19 vaccine with DHFF cost has also been carried out to validate out to validate our technique. In this article the proposed fuzzy system is included into this model to control uncertainties in Time, Quality, Cost, Reliability, and Availability induced in the transportation interruptions. The paper illustrates implication of the proposed fuzzy based model using a simulation in the context of a transportation process. The proposed model seeks to satisfy customers' demands for high-quality products and services, on a timely manner, at lowest cost possible. These characteristics are essential during times of disturbance, such as the COVID-19 pandemic.