Transportation optimization involves scrutinizing the mode of shipments, tariff, the purchasing policy, expectations, and demands of the supplier as well as the shopper with the hope of reducing the cost, time, and other transport objectives to make money which is an indispensable target for building a successful business. Among the mathematical tools available for handling impreciseness, a rough set has a simple mathematical structure in which preliminary information like statistical probability distribution, fuzzy membership grades are unneeded. In general, rough approximation utilizes the expected operators to alter the rough value into a crisp value for easier calculation and decisions. This gives only the average result but not the actual outcome which is risky. It is also sensitive in some extreme value cases. In this paper, the sure interval and the possible interval of each rough interval objective are fragmented into four crisp transportation problems, and the existing fuzzy programming approach is employed in a different manner to find the surely optimal and possibly optimal compromise solutions of the multi-objective rough transportation problem without utilizing the expected operator for the rough intervals. This approach is validated using numerical examples with bi-objectives and tri-objectives, which are solved using LINGO (19.0), and the results are compared.