Supply chain management is the nucleus of every organization which keeps an eye on the life cycle of each product from the stage of planning to distribution. Effective transportation is one among the vital parts of a successful supply chain and has a strong effect on the global economic development. The factors like speed, shipment density, geographical location of the source and destination, vehicle capacity and many others develop a parametric ambiguity in the transportation of goods and services. The disregarding of the above parameters may prompt business failure to an entrepreneur. Such a complexity can be dealt with soft sets which lends a detectable vision on the transportation budgeting. In this paper, a fuzzy soft multichoice multi-objective transportation model generated from the modal choice possibilities arising out of the three basic modes of transport namely roadways, railways, airways are investigated. The binary variable and lagrange interpolating polynomial approach are utilised for picking out the optimum objective value between each source and destination in the four possible modal options. In the end, an example for the fuzzy multichoice multi-objective soft transportation problem is solved with the existing weighted sum method (in LINGO 19.0) and the results from the two multichoice reduction approaches are stated.