A study on Uncertain four dimensional multi item multi objective fractional transportation problem

We often encounter problems that contain criteria that cannot be mutually proportioned. When we try to relate parameters, we can find that some of them are in the form of fractions. In this paper, we have presented a 4-dimensional multi-item multi objective fractional transport problem, the parameters of which are uncertain variables. Since the model is subject to uncertainty theory, the idea of maximization (minimization) according to the expectation of the objective function is formulated under a series of chance constraints. An equivalent deterministic model to four dimensional multi item multi objective fractional transportation model is obtained. Single objective function is formulated for all the uncertain fractional objectives of the proposed model. Furthermore, the presented model is solved to obtain its optimal solution. The numerical example is considered to have more clarity on the model.