Transportation Problem is widely studied in Operations Research field and mainly used to simulate different real-life problems. In real-world transportation planning, decision problems, input data and related parameters, such as available supply and forecast demand, are often imprecise /fuzzy because some information is incomplete or unavailable. Also, the decision maker must simultaneously handle conflicting goals that govern the use of constrained resources within organizations. The idea of a fuzzy set was first proposed by Zadeh in the year 1965, as a mean of handling uncertainty that is due to imprecision rather than randomness. Monte Carlo Method is used in fuzzy optimization problem to generate an approximate solution. Monte Carlo is a numerical method that makes use of the random number to solve a mathematical problem for which an analytical solution is not known, that is through random numbers experiment on the computer. Sobol set Quasi-random numbers are generated by using the Mat-lab code, which are distributed more uniformly in the given interval rather than the other types of random numbers. These random numbers are converted into fuzzy triangular random numbers in the interval [0, 1] and then converted them into the interval [a, b] by using the function (b-a)* r + a. Fuzzy number ≤ if each α – cut α is less than or equal to each α-cut α for any α > 0.5.